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Xin Cheng

Publications and source records attributed to Xin Cheng.

At least 37 records · Page 2Linked to original sources
arXiv2026

SeFi-Image: A Text-to-Image Foundation Model with Semantic-First Diffusion

Training image generation foundation models consumes substantial resources. Previous methods have attempted to leverage semantic guidance to accelerate the training process, yet their experiments were only conducted on simple datasets such as ImageNet, at low resolutions, and with small-scale models. In this paper, we propose SeFi-Image, a text-to-image foundation model built upon semantic-first diffusion, a novel latent diffusion modeling paradigm. We instantiate SeFi-Image at three model scales, 1B, 2B, and 5B parameters, enabling systematic study of scaling behavior and flexible deployment under varying compute budgets. Notably, our largest 5B model was trained with merely 125K A800 GPU hours, corresponding to roughly 10-20% of the training compute used by Z-Image. However, it achieves results comparable to or even superior to Qwen-Image and Z-Image. Despite this modest training compute, SeFi-Image achieves strong performance on a wide range of benchmarks, including GenEval, DPG, LongTextBench, OneIG, and CVTG-2K. Moreover, we provide DMD2-distilled few-step turbo variants for each model scale to accommodate diverse hardware constraints and latency requirements. We publicly release our code, weights and hope this work offers the community useful insights into semantic-guided diffusion modeling for T2I generation, while also providing practical and readily deployable model options.

cs.CV↗
arXiv2026

Joint Channel Estimation and Data Detection for Multi-LEO-Satellite Cell-Free OTFS Uplinks

Cell-free networks formed by multiple low Earth orbit (LEO) satellites offer a promising architecture for ubiquitous connectivity, but their cooperative reception is challenged by link-dependent residual delays and Doppler shifts. This paper investigates joint channel estimation and data detection (JCEDD) for multi-LEO-satellite cell-free orthogonal time frequency space (OTFS) uplinks. The JCEDD problem is formulated as a structured bilinear inference problem involving link-specific sparse beam--delay--Doppler channels and a multiuser data vector. We develop a low-complexity hierarchical JCEDD receiver in which all satellites first perform local JCEDD, and their observations and local estimates are then aggregated at a central satellite for cooperative refinement. Computational complexity is reduced by restricting channel estimation to coarse-information-aided local beam--delay--Doppler regions and evaluating the required forward and adjoint operations in a matrix-free manner. Simulation results validate the channel-estimation accuracy and data-detection reliability of the proposed JCEDD receiver.

eess.SP↗
arXiv2026

Conditional Memory via Scalable Lookup: A New Axis of Sparsity for Large Language Models

While Mixture-of-Experts (MoE) scales capacity via conditional computation, Transformers lack a native primitive for knowledge lookup, forcing them to inefficiently simulate retrieval through computation. To address this, we introduce conditional memory as a complementary sparsity axis, instantiated via Engram, a module that modernizes classic $N$-gram embedding for O(1) lookup. By formulating the Sparsity Allocation problem, we uncover a U-shaped scaling law that optimizes the trade-off between neural computation (MoE) and static memory (Engram). Guided by this law, we scale Engram to 27B parameters, achieving superior performance over a strictly iso-parameter and iso-FLOPs MoE baseline. Most notably, while the memory module is expected to aid knowledge retrieval (e.g., MMLU +3.4; CMMLU +4.0), we observe even larger gains in general reasoning (e.g., BBH +5.0; ARC-Challenge +3.7) and code/math domains~(HumanEval +3.0; MATH +2.4). Mechanistic analyses reveal that Engram relieves the backbone's early layers from static reconstruction, effectively deepening the network for complex reasoning. Furthermore, by delegating local dependencies to lookups, it frees up attention capacity for global context, substantially boosting long-context retrieval (e.g., Multi-Query NIAH: 84.2 to 97.0). Finally, Engram establishes infrastructure-aware efficiency: its deterministic addressing enables runtime prefetching from host memory, incurring negligible overhead. We envision conditional memory as an indispensable modeling primitive for next-generation sparse models.

cs.CL↗
arXiv2026

DSpark: Confidence-Scheduled Speculative Decoding with Semi-Autoregressive Generation

Speculative decoding accelerates Large Language Model (LLM) inference by decoupling draft generation from target verification. While recent parallel drafters efficiently propose long token sequences in a single forward pass, they suffer from rapid acceptance decay due to a lack of inter-token dependencies. Furthermore, indiscriminately verifying these extended blocks wastes critical batch capacity on tokens with high rejection risks, severely degrading throughput in high-concurrency serving systems. We introduce DSpark, a speculative decoding framework that unifies high-throughput parallel generation with adaptive, load-aware verification. To maintain draft quality, DSpark utilizes a semi-autoregressive architecture, coupling a parallel backbone with a lightweight sequential module, to introduce intra-block dependency modeling and mitigate suffix decay. To optimize system efficiency, DSpark employs confidence-scheduled verification, dynamically tailoring the verification length for each request based on estimated prefix survival probabilities and engine-specific throughput profiles. On offline benchmarks across diverse domains, DSpark substantially improves the accepted length over state-of-the-art autoregressive and parallel drafters. When deployed within the DeepSeek-V4 serving system under live user traffic, DSpark successfully mitigates verification waste. Compared to the established production baseline (MTP-1), DSpark accelerates per-user generation speeds by 60 to 85 percent at matched throughput levels. More importantly, by preventing severe throughput degradation under strict interactivity constraints, it enables performance tiers that were previously unattainable, shifting the Pareto frontier of our serving system.

cs.AI↗
arXiv2026

Taming Text-to-Sounding Video Generation via Advanced Modality Condition and Interaction

This study focuses on a challenging yet promising task, Text-to-Sounding-Video (T2SV) generation, which aims to generate a video with synchronized audio from text conditions, meanwhile ensuring both modalities are aligned with text. Despite progress in joint audio-video training, two critical challenges still remain unaddressed: (1) a single, shared text caption where the text for video is equal to the text for audio often creates modal interference, confusing the pretrained backbones, and (2) the optimal mechanism for cross-modal feature interaction remains unclear. To address these challenges, we first propose the Hierarchical Visual-Grounded Captioning (HVGC) framework that generates pairs of disentangled captions, a video caption, and an audio caption, eliminating interference at the conditioning stage. Based on HVGC, we further introduce BridgeDiT, a novel dual-tower diffusion transformer, which employs a Dual CrossAttention (DCA) mechanism that acts as a robust ``bridge" to enable a symmetric, bidirectional exchange of information, achieving both semantic and temporal synchronization. Extensive experiments on three benchmark datasets, supported by human evaluations, demonstrate that our method achieves state-of-the-art results on most metrics. Comprehensive ablation studies further validate the effectiveness of our contributions, offering key insights for the future T2SV task. All the codes and checkpoints will be publicly released.

cs.CV↗
arXiv2026

AgenticOS: An Intent-Oriented Secure Operating System Architecture for Autonomous AI Agents

Traditional OS security models based on "resource exposure plus permission checks" face structural challenges as LLM-driven autonomous agents acquire capabilities for planning, tool use, network access, and code execution. Once an agent runtime is compromised through prompt injection or malicious tool outputs, an attacker can compose POSIX-style resource primitives into behaviors far beyond the user's task authorization. To address this, we propose AgenticOS, an intent-oriented secure OS architecture that consolidates delegable, auditable software capabilities into OS-native ones rather than replacing all applications. The core insight is to reframe the OS from a "resource manager" into an "intent filter": instead of requesting low-level resources directly, agents submit structured intent declarations, from which the system synthesizes a least-privilege environment with mandatory mediation, auditing, and information-flow constraints. At the implementation level, we introduce a four-layer architecture -- Ghost Kernel, Logic Shutter, Agent Capsule, and Semantic Boundary Gateway -- together with the Intent ABI, Manifest-Only Runtime, Weaver-based capability generation, and an admission model for AgenticOS-native Skills.

cs.CR↗
arXiv2026

Beyond Trajectory-Level Attribution: Graph-Based Credit Assignment for Agentic Reinforcement Learning

Group-based reinforcement learning (RL) methods have achieved remarkable success in improving the performance of large language models (LLMs) and have been rapidly extended to agentic tasks. However, their credit assignment relies heavily on coarse-grained trajectory-level attribution according to final outcomes, making it difficult to capture the contribution of individual steps, such as valuable steps obscured within failed trajectories. To uncover latent information and enable more faithful step-level credit assignment, we propose Graph-based Group Policy Optimization (GraphGPO), which first aggregates all rollout trajectories into a unified state-transition graph and then estimates the distance from each state to the task goal using the global information encoded in the graph. Finally, GraphGPO assigns credit to each edge by estimating a graph-based advantage, based on how much the transition reduces the distance to the task goal. In this way, GraphGPO significantly improves training efficiency and achieves state-of-the-art performance across a range of challenging benchmarks.

cs.LG↗
arXiv2026

Unified Synthesis of Compositional Speech and Sound from Free-Form Text Prompts

Audio generation has made significant progress, yet synthesizing unified audio where speech and sounds are naturally composited remains a challenge. Current methods either rely on disjoint pipelines, which fail to capture fine-grained interactions, or require structured inputs and external text rewriting, which limits the flexibility of free-form text prompts. In this paper, we introduce a new task: Free-Form-Text-Prompt-to-Unified-Audio generation, which aims to directly synthesize unified audio containing speech, sound, and their composites from unconstrained natural language. To address this task, we propose PlanAudio, a unified, autoregressive LLM-based framework. First, it simplifies the model architecture by leveraging intrinsic LLM reasoning capability instead of traditional text encoders. Second, it introduces a semantic latent chain-of-thought mechanism, an implicit planning mechanism that bridges high-level semantic understanding and low-level acoustic synthesis. Furthermore, we create PlanAudio-Bench, a specialized benchmark for evaluating composite audio scenarios. We perform evaluations in the scenarios of speech, sound, and their composites. The results demonstrate that PlanAudio generally outperforms the existing pipeline and unified baselines, while staying competitive with models designed for a single scenario. Our analysis further reveals the superiority of semantic latent CoT over other CoT mechanisms and highlights the importance of continuous multi-scenario training curricula.

cs.SD↗
arXiv2026

On the Turán number of blow-ups of $\mathcal{F}_5$

Let $\mathcal{F}_5$ denote the $3$-uniform hypergraph on the vertex set $\{f_1,f_2,\dots,f_5\}$ with hyperedges $\{f_1f_2f_3,f_1f_2f_4,f_3f_4f_5\}$. Recently, Balogh, Clemen and Luo determined the Turán number of a one-vertex blow-up of $\mathcal{F}_5$, more specifically, they blow up the vertex $f_5$ to $t$ vertices, the resulting hypergraph is denoted by $\mathcal{F}_5(f_5;t)$. They show that for infinitely many $t$, $\mathcal{F}_5(f_5;t)$ has exponentially many extremal constructions and positive Turán density. In this paper, we determine the exact Turán number of the hypergraph obtained by blowing up $f_3$ of $\mathcal{F}_5$ to $t$ vertices and show that it also has exponentially many extremal constructions. We also give a general upper bound and lower bound of the Turán number of every blow-up of $\mathcal{F}_5$. For some special blow-ups of $\mathcal{F}_5$, for example, $t$-disjoint copies of $\mathcal{F}_5$, we determine the exact Turán number. We construct a hypergraph $\mathcal{F}_{sim}(t)$ which is a subgraph of a blow-up of $\mathcal{F}_5$, and is contained in the hypergraph obtained by adding any new hyperedge to the Turán hypergraph (the balanced complete $3$-partite hypergraph), but its extremal construction is not the Turán hypergraph. We also determine the exact Turán number of $\mathcal{F}_{sim}(t)$.

math.CO↗
arXiv2026

SyncDPO: Enhancing Temporal Synchronization in Video-Audio Joint Generation via Preference Learning

Recent advancements in video-audio joint generation have achieved remarkable success in semantic correspondence. However, achieving precise temporal synchronization, which requires fine-grained alignment between audio events and their visual triggers, remains a challenging problem. The post-training method for joint generation is largely dominated by Supervised Fine-Tuning, but the commonly used Mean Squared Error loss provides insufficient penalties for subtle temporal misalignments. Direct Preference Optimization offers an alternative by introducing explicit misaligned counterparts to better improve temporal sensitivity. In this paper we propose a post-training framework SyncDPO, leveraging DPO to improve the temporal sensitivity of V-A joint generation. Conventional DPO pipelines typically depend on costly sampling-and-ranking procedures to construct preference pairs, resulting in substantial computational cost. To improve efficiency, we introduce a suite of on-the-fly rule-based negative construction strategies that distort temporal structures without incurring additional annotation or sampling. We demonstrate that the temporal alignment capability can be effectively reinforced by providing explicit negative supervision through temporally distorted V-A pairs. Accordingly, we implement a curriculum learning strategy that progressively increases the difficulty of negative samples, transitioning from coarse misalignment to subtle inconsistencies. Extensive objective and subjective experiments across four diverse benchmarks, ranging from ambient sound videos to human speech videos, demonstrate that SyncDPO significantly outperforms other methods in improving model's temporal alignment capability. It also demonstrates superior generalization on out-of-distribution benchmark by capturing intrinsic motion-sound dynamics. Demo and code is available in https://syncdpo.github.io/syncdpo/.

cs.CV↗
arXiv2026

VertMark: A Unified Training-Free Robust Watermarking Framework for Vertical Domain Pre-trained Language Models

With the application of vertical domain pre-trained language models (VPLMs) in specialized fields such as medical, finance, and law, model parameters and inference capabilities have become important digital assets. Achieving traceable copyright verification for VPLMs has become an urgent challenge. Existing copyright verification methods primarily rely on embedding backdoor watermarks into models. However, most of these methods require additional training, suffer from inefficient watermark embedding, and lack scalable designs for multiple vertical domains. To address these limitations, we propose VertMark, the first unified training-free and robust watermarking framework for copyright verification across multiple vertical domain VPLMs. The framework embeds ownership-encoded watermarks by establishing a hidden semantic equivalence between low-frequency trigger tokens and high-frequency domain-relevant words via a training-free parameter replacement strategy. Experiments demonstrate that VertMark can achieve efficient watermark embedding and reliable watermark verification for both text understanding and text generation downstream tasks in the medical, financial, and legal domains, with negligible impact on model performance. Moreover, VertMark exhibits strong robustness against various attacks (e.g., pruning and quantization), highlighting its practical value and providing strong protection for the copyright security of VPLMs.

cs.CR↗
arXiv2026

Generalized Turán problems for Berge hypergraphs

Let $\mathcal{H}$ be a hypergraph and $F$ be a graph. If there exists a bijection between the hyperedges of $\mathcal{H}$ and the edges of $F$ such that each hyperedge contains its image, then we say that $\mathcal{H}$ is a \textit{Berge copy} of $F$, and the collection of Berge copies of $F$ is denoted by Berge-$F$. Given $r$-graphs $\mathcal{F}$ and $\mathcal{H}$, the generalized hyper-Turán number $\text{ex}_r(n, \mathcal{H}, \mathcal{F})$ is the maximum number of copies of $\mathcal{H}$ in $n$-vertex $\mathcal{F}$-free $r$-graphs. We study $\text{ex}_r(n, \mathcal{H}, \text{Berge-}F)$. For general $\mathcal{H}$, we connect this problem to counting copies of the shadow graph of $\mathcal{H}$ in $F$-free graphs and obtain several exact results. In particular, we show that for any hypergraph $\mathcal{H}$, if $k$ is sufficiently large, then $\text{ex}_r(n, \mathcal{H}, \text{Berge-}K_k)$ is achieved by the balanced complete $(k-1)$-partite $r$-graph, generalizing a result of Morrison, Nir, Norin, Rza{ż}ewski and Wesolek [\textit{Journal of Combinatorial Theory, Series B}, 162 (2023) 231--243] to the case of hypergraphs. We show that $\text{ex}_r(n,K_s^r,\text{Berge-}F)\le \text{ex}_s(n,\text{Berge-}F)$ and present sufficient conditions for equality. We also consider the connected generalized Turán number for Berge paths.

math.CO↗
arXiv2026

The Turán number of the Cartesian product of a star and an edge

Let $C_k$ denote the cycle of length $k$, $S_t$ be a star with $t$ edges. And let $B_t$ be the graph consisting of $t$ copies of $C_4$ sharing one fixed edge. Equivalently, $B_t=K_2 \mathbin{\square} S_t$, which is the Cartesian product of a star with $t$ edges and an edge. Recently, Gao, Janzer, Liu and Xu [\textit{Israel J. Math. 269(2025)}] proved that the Turán number of $K_2\mathbin{\square} C_{2l}$ is $Θ(n^{\frac{3}{2}})$ for every $l\ge 4$. In this paper, we obtain upper and lower estimates for the Turán number of $B_t$ in both the general and bipartite settings for every $t\geq 2$. For the lower bound, we use random construction based on the extremal structure of $C_4$. These results imply that $\frac{1}{2\sqrt{2}}\leq \lim_{t\to \infty} \frac{\mathrm{ex}(n,B_t)}{\sqrt{t}}\leq \frac{1}{2}$, and $\frac{1}{4}\leq \lim_{t\to \infty} \frac{\mathrm{ex}_{bip}(n,B_t)}{\sqrt{t}}\leq \frac{1}{2\sqrt{2}}.$ In the case of $B_2$, we obtain sharper estimates. We show that the Turán number of $B_2$ is approximately between $(0.518+o(1))n^{\frac{3}{2}}$ and $(0.603+o(1))n^{\frac{3}{2}}$. And in the bipartite setting, it is approximately between $(0.385+o(1))n^{\frac{3}{2}}$ and $(0.468+o(1))n^{\frac{3}{2}}$. Moreover, in the bipartite setting, we give a more general result, which shows that for every tree $T$ with $t$ edges, the bipartite Turán number of $K_2\mathbin{\square}T$ is at most $\frac{\sqrt{t}}{2\sqrt{2}}(1+o(1))n^{\frac{3}{2}}$.

math.CO↗
arXiv2026

Forbidding matching as trace in uniform hypergraphs

We say a hypergraph $\mathcal{H}$ contains a hypergraph $\mathcal{G}$ as trace if there exists a vertex subset $S \subseteq V(\mathcal{H})$ such that $|S| = |V(\mathcal{G})|$ and $\{e \cap S: e \in E(\mathcal{H})\}$ contains $\mathcal{G}$ as a sub-hypergraph. We use $\mathrm{ex}_r(n, \mathrm{Tr}_r(\mathcal{G}))$ to denote the maximum number of hyperedges in an $r$-uniform hypergraph on $n$ vertices not containing $\mathcal{G}$ as a trace. The study of Turán numbers for traces was initiated by Mubayi and Zhao who studied the case when $\mathcal{G}$ is a complete graph. Let $M_{s+1}$ denote the graph of a matching with $s+1$ edges. In this paper, we give the upper bound of $\mathrm{ex}_r(n, \mathrm{Tr}_r(M_{s+1}))$ which is sharp asymptotically. When $r=3$, we give the exact value of $\mathrm{ex}_3 (n, \mathrm{Tr}_3 (M_{s+1}))$. We also consider the generalized Turán number in the case of matching. That is, the maximum number of copies of clique $\mathcal{K}_t^r$ in hypergraphs forbidding $\mathrm{Tr}_r (M_{s+1})$ as a trace. We give an upper bound which is sharp asymptotically and when $r=3$, we give the exact value. The Turán number of forbidding a matching and the other graph is another well studied topic initiated by Alon and Frankl. We also consider an analogue problem for the trace version, i.e., forbidding trace of matching and trace of complete graph as subgraphs.

math.CO↗
arXiv2026

CUTEv2: Unified and Configurable Matrix Extension for Diverse CPU Architectures with Minimal Design Overhead

Matrix extensions have emerged as an essential feature in modern CPUs to address the surging demands of AI workloads. However, existing designs often incur substantial hardware and software design overhead. Tight coupling with the CPU pipeline complicates integration across diverse CPUs, while fine-grained synchronous instructions hinder the development of high-performance kernels. This paper proposes a unified and configurable CPU matrix extension architecture. By decoupling matrix units from the CPU pipeline, the design enables low-overhead integration while maintaining close coordination with existing compute and memory resources. The configurable matrix unit supports mixed-precision operations and adapts to diverse compute demands and memory bandwidth constraints. An asynchronous matrix multiplication abstraction with flexible granularity conceals hardware details, simplifies matrix-vector overlap, and supports a unified software stack. The architecture is integrated into four open-source CPU RTL platforms and evaluated on representative AI models. Matrix unit utilization under GEMM workloads exceeds 90% across all platforms. When configured with compute throughput and memory bandwidth comparable to Intel AMX, our design achieves speedups of 1.57x, 1.57x, and 2.31x on ResNet, BERT, and Llama3, with over 30% of the gains attributed to overlapped matrix-vector execution. A 4 TOPS@2GHz matrix unit occupies only 0.53 mm\textsuperscript{2} in 14nm CMOS. These results demonstrate strong cross-platform adaptability and effective hardware-software co-optimization, offering a practical matrix extension for the open-source community.

cs.AR↗
arXiv2026

VSSFlow: Unifying Video-conditioned Sound and Speech Generation via Joint Learning

Video-conditioned audio generation, including Video-to-Sound (V2S) and Visual Text-to-Speech (VisualTTS), has traditionally been treated as distinct tasks, leaving the potential for a unified generative framework largely underexplored. In this paper, we bridge this gap with VSSFlow, a unified flow-matching framework that seamlessly solve both problems. To effectively handle multiple input signals within a Diffusion Transformer (DiT) architecture, we propose a disentangled condition aggregation mechanism leveraging distinct intrinsic properties of attention layers: cross-attention for semantic conditions, and self-attention for temporally-intensive conditions. Besides, contrary to the prevailing belief that joint training for the two tasks leads to performance degradation, we demonstrate that VSSFlow maintains superior performance during end-to-end joint learning process. Furthermore, we use a straightforward feature-level data synthesis method, demonstrating that our framework provides a robust foundation that easily adapts to joint sound and speech generation using synthetic data. Extensive experiments on V2S, VisualTTS and joint generation benchmarks show that VSSFlow effectively unifies these tasks and surpasses state-of-the-art domain-specific baselines, underscoring the critical potential of unified generative models. Project page: https://vasflow1.github.io/vasflow/

eess.AS↗
arXiv2026

Online Causal Kalman Filtering for Stable and Effective Policy Optimization

Reinforcement learning for large language models suffers from high-variance token-level importance sampling (IS) ratios, which would destabilize policy optimization at scale. To improve stability, recent methods typically use a fixed sequence-level IS ratio for all tokens in a sequence or adjust each token's IS ratio separately, thereby neglecting temporal off-policy derivation across tokens in a sequence. In this paper, we first empirically identify that local off-policy deviation is structurally inconsistent at the token level, which may distort policy-gradient updates across adjacent tokens and lead to training collapse. To address the issue, we propose Online Causal Kalman Filtering for stable and effective Policy Optimization (KPO). Concretely, we model the desired IS ratio as a latent state that evolves across tokens and apply a Kalman filter to update this state online and autoregressively based on the states of past tokens, regardless of future tokens. The resulting filtered IS ratios preserve token-wise local structure-aware variation while strongly smoothing noise spikes, yielding more stable and effective policy updates. Experimentally, KPO achieves superior results on challenging math reasoning datasets compared with state-of-the-art counterparts.

cs.CL↗
arXiv2026

Forbidding edge-critical graphs as trace in uniform hypergraphs

We say a hypergraph $\mathcal{H}$ contains a graph $G$ as trace if there exists a vertex subset $S \subseteq V(\mathcal{H})$ such that $|S| = V(G)$ and $\{e \cap S \mid e \in E(\mathcal{H})\}$ contains $G$ as a subgraph. We use $\mathrm{ex}(n, Tr_r(G))$ to denote the maximum number of edges in an $r$-uniform hypergraph on $n$ vertices not containing $G$ as trace. The study of Turán numbers for traces was initiated by Mubayi and Zhao~(2017) who studied $\mathrm{ex}(n, Tr_r(K_{s+1}))$ where $K_{s+1}$ is a clique on $s+1$ vertices and conjectured the exact value of $\mathrm{ex}(n, Tr_r(K_{s+1}))$. When $r \le s$, the conjecture was covered by a result of Pikhurko~(2013) who gave the exact value of Turán numbers for expanded cliques. Then Gerbner and Picollelli~(2023) gave the exact value for book graphs~($K_{1,1,t}$, the complete tripartite graph with two parts of size one and one part of size $t \ge 2$). We say $G$ is edge-critical if there exists an edge $e \in E(G)$ such that $χ(G - e) < χ(G)$ where $χ(G)$ is the chromatic number of $G$. The definition of edge-critical was given by Simonovits~(1974), who proved that for an edge-critical graph $G$ with $χ(G) = s+1 \ge 3$, the Turán graph $T(n,s)$ is the unique extremal graph for $ex(n,G)$ as $n$ is sufficiently large. In this paper, we further generalize the results of Gerbner and Picollelli~(2023) to edge-critical graphs. More precisely, we prove that for an edge-critical graph $G$ with $χ(G) = s+1$, when $s \ge r \ge 3$ and $n$ is sufficiently large, the $r$-uniform Turán graph $T_r(n,s)$ is the unique extremal hypergraph.

math.CO↗