arXiv subjects

Jiaao Li

Publications and source records attributed to Jiaao Li.

At least 19 recordsLinked to original sources

arXiv2026

Nowhere-zero $3$-flows in graphs with forbidden edge-cuts

Tutte's $3$-flow conjecture asserts that every $4$-edge-connected graph admits a nowhere-zero $3$-flow. In 2013, Lovász, Thomassen, Wu, and Zhang proved that every odd-$7$-edge-connected graph admits a nowhere-zero $3$-flow; consequently, the conjecture holds for $4$-edge-connected graphs with no edge-cut of size $5$. We consider the complementary situation in which $5$-edge-cuts are allowed. We show that, when edge-cuts of size $5$ are permitted, Tutte's $3$-flow conjecture holds for graphs with no edge-cut of any size from $6$ to $k$, where $k$ is an absolute constant. In fact, $k=40$ suffices and we prove a stronger version in which only nontrivial edge-cuts of those sizes are forbidden. A graph is called essentially $t$-edge-connected if deleting any set of at most $t-1$ edges leaves at most one nontrivial component. Motivated by Jaeger's weak $3$-flow conjecture, we prove an analogous result for essential edge connectivity: every $4$-edge-connected, essentially $41$-edge-connected graph admits a nowhere-zero $3$-flow.

math.CO↗

arXiv2026

B-coloring of grid graphs

A B-coloring of a graph $G$ is a proper edge-coloring in which every $4$-cycle is rainbow. Let $q_B(G)$ be the minimum number of colors in such a coloring. Gyárfás and Sárközy (2023) determine $q_B(G)$ when $G=P_m\square P_n$ is a rectangular grid. In this paper, we completely determine $q_B(G)$ for cylindrical and torus grid graphs $G$. For a torus grid $G=C_m\square C_n$, where $m,n\ge3$ are integers, we prove that $q_B(G)=4=Δ(G)$ if both $m$ and $n$ are even and $G\not\cong C_4\square C_{4k+2}$ for any integer $k\ge1$, and that $q_B(G)=5=Δ(G)+1$ if at least one of $m,n$ is odd or $G\cong C_4\square C_{4k+2}$ for some integer $k\ge1$. For a cylindrical grid $G=C_s\square P_m$, $q_B(G)$ also depends on the parity of $s$ and the length of $P_m$. For integers $m\ge2$ and $n\ge2$, we have $q_B(C_{2n}\square P_m)=4$. For integers $m\ge2$ and $n\ge1$, we have $q_B(C_{2n+1}\square P_m)=4$ if $2\le m\le n$, whereas $q_B(C_{2n+1}\square P_m)=5$ if $m\ge n+1$. In higher dimensions, we discuss the B-coloring of discrete torus and $\ell$-cylindrical grid, obtaining some exact results and certain bounds.

math.CO↗

arXiv2026

Anchoring Instruction Outside Mask: Exact Reference Caching for Efficient In-Context Diffusion Transformers

Omnimodal generation is central to a wide range of content creation and editing applications. In-context conditioning is essential to this paradigm. It allows diffusion transformers to process text instructions and visual references in a shared attention sequence. However, each reference image introduces thousands of tokens. Computation therefore grows rapidly with the number of references. Existing methods reduce computation through structured sparse attention, which limits interactions between reference and target tokens. This structure also makes the reference K and V independent of the denoising target, allowing them to be computed once and reused across steps. However, it blocks visual references from attending to the text instruction. This substantially degrades instruction following and reference fidelity in multi-reference editing. To resolve this conflict, we jointly redesign the token sequence and attention mask. Our beyond-mask design uses static text anchors to connect the instruction to the reference branch. It preserves exact K and V reuse without adding parameters. However, this direct architectural conversion degrades generation quality. We recover the lost performance through teacher-forced velocity distillation, followed by a short on-policy stage in which the teacher supervises student-visited states. To our knowledge, this is the first use of on-policy distillation for architectural recovery in diffusion models. Across three image-editing benchmarks, our method matches full-attention generation quality. With five reference images, it accelerates the complete 40-step denoising process by 3.92x, while static text anchors introduce negligible runtime overhead; the speedup reaches 5.47x at ten references in our scaling study.

cs.CV↗

arXiv2026

A local clique density theorem in $H$-free graphs

In 2016, Reiher's clique density theorem determined the minimum number of copies of $K_t$ in a graph with a prescribed edge density. In this paper, we investigate its local version and prove a local clique density theorem in $H$-free graphs as follows. For integers $r$ and $t$ with $2\leq t\leq r-1$, any $r$-chromatic graph $H$, any real numbers $γ$ and $α$ with $\frac{t-2}{2(t-1)}\leqγ\leq \frac{r-2}{2(r-1)}$ and $0\leqα\leq 1$, we determine the maximum value $β:=β(r,t,α,γ)$ such that for every $n$-vertex $H$-free graph $G$ with at least $γn^2$ edges, every $\lceilαn\rceil$-vertex subset in $G$ contains at least $(β-o(1))n^{t}$ copies of $K_t$. In particular, when $H=K_r$, every $\lceilαn\rceil$-vertex subset contains at least $\lfloorβn^t\rfloor$ copies of $K_t$, which is an exact bound. For suitable choices of $α$ and $γ$, namely, those for which all part ratios in the corresponding extremal construction are rational, this bound is attained for infinitely many values of $n$.

math.CO↗

arXiv2026

Reduction Operations and Structural Characterizations of $S^1$-Flows in Graphs

While every graph admitting a nowhere-zero $3$-flow also admits an $S^1$-flow, the converse does not hold in general as shown by Thomassen (2014). In this paper, we develop reduction techniques for $S^1$-flows based on graph operations including bull-growth, $2$-sums, and wheel contractions. A key tool is the two-terminal $S^1$-preflow, which enables us to prove that if a $2$-connected graph contains an odd wheel as a proper subgraph and contracting the wheel yields a graph with a nowhere-zero $3$-flow, then the original graph admits an $S^1$-flow. As applications, we completely characterize $S^1$-flows in two graph classes: a triangularly connected graph admits an $S^1$-flow if and only if it is not an odd wheel; and a graph containing a spanning triangle-tree admits an $S^1$-flow if and only if it is not an odd crystal.

math.CO↗

arXiv2026

Orientations of $10$-Edge-Connected Planar Multigraphs and Applications

A graph is called strongly $\Z_{2k+1}$-connected if for each boundary function $β: V(G)\mapsto \Z_{2k+1}$ with $\sum_{v\in V(G)}β(v)\equiv 0\pmod{2k+1}$, there exists an orientation $D$ of $G$ such that $d_D^+(v) - d_D^-(v) \equiv β(v) \pmod{2k+1}$ for each $v \in V(G)$. We show that every planar multigraph with $5$ edge-disjoint spanning trees is strongly $\Z_{5}$-connected. This verifies a special case of the Additive Base Conjecture when restricted to planar graphs. Hence, every $10$-edge-connected directed planar graph admits an antisymmetric $\Z_5$-flow. So, by duality, every orientation of a planar graph of girth at least $10$ admits a homomorphism to a $5$-vertex tournament. Our result also gives a new proof of the known result that every planar graph of girth at least $10$ has a homomorphism to the $5$-cycle.

math.CO↗

arXiv2026

Frustration index of a signed planar graph and the feedback vertex set

A feedback vertex set of a graph is a set of vertices whose deletion leaves a forest. In 2016, Dross, Montassier, and Pinlou conjectured that every planar graph $G$ of girth at least $g$ admits a feedback vertex set of size at most $e(G)/g$. In this note, we confirm this conjecture by connecting this problem with signed graphs. The frustration index of a signed graph $(G,Σ)$ is defined as the minimum number of negative edges among all signatures on $G$ that are switching-equivalent to $Σ$. Equivalently, it is the minimum number of edges whose deletion results in a balanced subgraph of $(G,Σ)$. We show that the minimum size of a feedback vertex set of a planar graph is bounded above by the maximum frustration index over all signatures of the graph, and thereby provide a tight upper bound on the size of the minimum feedback vertex set, which resolves the conjecture of Dross, Montassier, and Pinlou (2016).

math.CO↗

arXiv2026

Reconfiguration of Nowhere-zero Flows

Fix an abelian group $A$, a graph $G$, and nowhere-zero $A$-flows $f'$ and $f''$ on $G$. Now $f'$ and $f''$ are \emph{$A$-flow-adjacent} if there exists a cycle $C$ in $G$ such that $f'(e)-f''(e)=0$ for all edges $e\notin E(C)$. And $f'$ and $f''$ are \emph{$A$-flow-equivalent} if there exists a sequence $f_0,\ldots,f_s$ of $A$-flows such that $f_0=f'$, $f_s=f''$, and $f_i$ and $f_{i-1}$ are $A$-flow-adjacent for all $i\in[s]$. Given a group $A$, we seek conditions on a graph $G$ such that all $A$-flows on $G$ are pairwise $A$-flow-equivalent; in this case, we say that $G$ is \emph{$A$-flow-connected}. Analogously, we define $k$-flow-connectedness for nowhere-zero (integer) $k$-flows. The notions of $A$-flow-connectedness and $k$-flow-connectedness were first investigated by Esperet et al., who showed, among other results, that every $2$-edge-connected graph is $A$-flow-connected whenever $A=\mathbb{Z}_2^8$ or $|A| \ge 1.15\times 10^{694}$. In this paper, we first characterize the graphs that are $\mathbb{Z}_3$-flow-connected and that are $3$-flow-connected. We show that every 2-edge-connected graph is $A$-flow-connected if and only if this is true for every 2-edge-connected cubic graphs. We show that all cubic bipartite graphs are $\mathbb{Z}_4$-flow-connected, and construct other cubic graphs that are and are not $\mathbb{Z}_4$-flow-connected. We conjecture that every Eulerian graph is $k$-flow-connected and $A$-flow-connected whenever $k$ or $|A|$ is even; and provide evidence for this conjecture. Finally, we consider $4$-edge-connected graphs $G$. Here, we show that $G$ is $A$-flow-connected whenever $|A|\ge 5.3\times 10^6$.

math.CO↗

arXiv2026

Characterization of strongly $\mathbb{Z}_\ell$-connected graphs of small order

A graph is strongly $\Z_{\ell}$-connected if for each boundary function $β: V(G)\mapsto \Z_{\ell}$ with $β(v) \equiv d(v) \pmod{2}$ for every vertex $v$ and $\sum_{v \in V(G)} β(v) \equiv 0 \pmod{2\ell}$, there exists an orientation $D$ of $G$ such that $d_D^+(v) - d_D^-(v) \equiv β(v) \pmod{2\ell}$ for each $v \in V(G)$. This is a useful notion for studying circular flows of graphs. This note presents a fully self-contained, manual proof of a characterization of $4$-vertex strongly $\mathbb{Z}_\ell$-connected graphs for any integer $\ell\geq 2$, which will be used in our further study in this topic.

math.CO↗

arXiv2026

High-Dimensional $p$-Normed Flows

We generalize Tutte's integer flows and the $d$-dimensional Euclidean flows of Mattiolo, Mazzuoccolo, Rajník, and Tabarelli to \emph{$d$-dimensional $p$-normed nowhere-zero flows} and define the corresponding flow index $ϕ_{d,p}(G)$ to be the infimum over all real numbers $r$ for which $G$ admits a $d$-dimensional $p$-normed nowhere-zero $r$-flow. For any bridgeless graph $G$ and any $p\ge 1$, we establish general upper bounds, including $ϕ_{2,p}(G) \le 3$, $ϕ_{3,p}(G) \le 1+\sqrt{2}$, and tight bounds for graphs admitting a $4$-NZF. For graphs with oriented $(k+1)$-cycle $2l$-covers, we show that $ϕ_{k,p}(G) = 2$, which implies $ϕ_{2,p}(G) = 2$ for graphs admitting a nowhere-zero $3$-flow and $ϕ_{3,p}(G) = 2$ for those admitting a nowhere-zero $4$-flow. These results extend classical flow theory to arbitrary norms, provide supporting evidences for Tutte's $5$-flow Conjecture and Jain's $S^2$-Flow Conjecture, and connect combinatorial flows with geometric and topological perspectives.

math.CO↗

arXiv2025

Frustration indices of signed subcubic graphs

The frustration index of a signed graph is defined as the minimum number of negative edges among all switching-equivalent signatures. This can be regarded as a generalization of the classical \textsc{Max-Cut} problem in graphs, as the \textsc{Max-Cut} problem is equivalent to determining the frustration index of signed graphs with all edges being negative signs. In this paper, we prove that the frustration index of an $n$-vertex signed connected simple subcubic graph, other than $(K_4, -)$, is at most $\frac{3n + 2}{8}$, and we characterize the family of signed graphs for which this bound is attained. This bound can be further improved to $\frac{n}{3}$ for signed $2$-edge-connected simple subcubic graphs, with the exceptional signed graphs being characterized. As a corollary, every signed $2$-edge-connected simple cubic graph on at least $10$ vertices and with $m$ edges has its frustration index at most $\frac{2}{9}m$, where the upper bound is tight as it is achieved by an infinite family of signed cubic graphs.

math.CO↗

arXiv2025

XplaiNLP at CheckThat! 2025: Multilingual Subjectivity Detection with Finetuned Transformers and Prompt-Based Inference with Large Language Models

This notebook reports the XplaiNLP submission to the CheckThat! 2025 shared task on multilingual subjectivity detection. We evaluate two approaches: (1) supervised fine-tuning of transformer encoders, EuroBERT, XLM-RoBERTa, and German-BERT, on monolingual and machine-translated training data; and (2) zero-shot prompting using two LLMs: o3-mini for Annotation (rule-based labelling) and gpt-4.1-mini for DoubleDown (contrastive rewriting) and Perspective (comparative reasoning). The Annotation Approach achieves 1st place in the Italian monolingual subtask with an F_1 score of 0.8104, outperforming the baseline of 0.6941. In the Romanian zero-shot setting, the fine-tuned XLM-RoBERTa model obtains an F_1 score of 0.7917, ranking 3rd and exceeding the baseline of 0.6461. The same model also performs reliably in the multilingual task and improves over the baseline in Greek. For German, a German-BERT model fine-tuned on translated training data from typologically related languages yields competitive performance over the baseline. In contrast, performance in the Ukrainian and Polish zero-shot settings falls slightly below the respective baselines, reflecting the challenge of generalization in low-resource cross-lingual scenarios.

cs.CL↗

arXiv2025

Multilingual Datasets for Custom Input Extraction and Explanation Requests Parsing in Conversational XAI Systems

Conversational explainable artificial intelligence (ConvXAI) systems based on large language models (LLMs) have garnered considerable attention for their ability to enhance user comprehension through dialogue-based explanations. Current ConvXAI systems often are based on intent recognition to accurately identify the user's desired intention and map it to an explainability method. While such methods offer great precision and reliability in discerning users' underlying intentions for English, a significant challenge in the scarcity of training data persists, which impedes multilingual generalization. Besides, the support for free-form custom inputs, which are user-defined data distinct from pre-configured dataset instances, remains largely limited. To bridge these gaps, we first introduce MultiCoXQL, a multilingual extension of the CoXQL dataset spanning five typologically diverse languages, including one low-resource language. Subsequently, we propose a new parsing approach aimed at enhancing multilingual parsing performance, and evaluate three LLMs on MultiCoXQL using various parsing strategies. Furthermore, we present Compass, a new multilingual dataset designed for custom input extraction in ConvXAI systems, encompassing 11 intents across the same five languages as MultiCoXQL. We conduct monolingual, cross-lingual, and multilingual evaluations on Compass, employing three LLMs of varying sizes alongside BERT-type models.

cs.CL↗

arXiv2025

Hybrid Annotation for Propaganda Detection: Integrating LLM Pre-Annotations with Human Intelligence

Propaganda detection on social media remains challenging due to task complexity and limited high-quality labeled data. This paper introduces a novel framework that combines human expertise with Large Language Model (LLM) assistance to improve both annotation consistency and scalability. We propose a hierarchical taxonomy that organizes 14 fine-grained propaganda techniques into three broader categories, conduct a human annotation study on the HQP dataset that reveals low inter-annotator agreement for fine-grained labels, and implement an LLM-assisted pre-annotation pipeline that extracts propagandistic spans, generates concise explanations, and assigns local labels as well as a global label. A secondary human verification study shows significant improvements in both agreement and time-efficiency. Building on this, we fine-tune smaller language models (SLMs) to perform structured annotation. Instead of fine-tuning on human annotations, we train on high-quality LLM-generated data, allowing a large model to produce these annotations and a smaller model to learn to generate them via knowledge distillation. Our work contributes towards the development of scalable and robust propaganda detection systems, supporting the idea of transparent and accountable media ecosystems in line with SDG 16. The code is publicly available at our GitHub repository.

cs.CL↗

arXiv2025

EgoPrune: Efficient Token Pruning for Egomotion Video Reasoning in Embodied Agent

Egomotion videos are first-person recordings where the view changes continuously due to the agent's movement. As they serve as the primary visual input for embodied AI agents, making egomotion video reasoning more efficient is therefore essential for real-world deployment. Recent advances in vision-language models have enabled strong multimodal reasoning capabilities, but their computational cost remains prohibitive for long, redundant video inputs. Existing token pruning methods, typically designed for third-person videos, fail to leverage the spatiotemporal continuity and motion constraints inherent in egomotion settings. To address this, we propose EgoPrune, a training-free token pruning method tailored for egomotion video reasoning. EgoPrune comprises three components: a keyframe selector adapted from EmbodiedR for temporally efficient sampling; Perspective-Aware Redundancy Filtering (PARF), which aligns visual tokens using perspective transformations and removes redundant tokens; and a Maximal Marginal Relevance (MMR)-based token selector that jointly considers visual-text relevance and intra-frame diversity. Experiments on two egomotion video benchmarks show that EgoPrune consistently outperforms prior training-free methods across various pruning ratios while significantly reducing FLOPs, memory usage, and latency. Moreover, we deploy EgoPrune on an embodied agent equipped with a Jetson Orin NX 16GB edge device, demonstrating its real-world efficiency and suitability for on-device egomotion video reasoning.

cs.CV↗

arXiv2025

Fast SSVEP Detection Using a Calibration-Free EEG Decoding Framework

Steady-State Visual Evoked Potential is a brain response to visual stimuli flickering at constant frequencies. It is commonly used in brain-computer interfaces for direct brain-device communication due to their simplicity, minimal training data, and high information transfer rate. Traditional methods suffer from poor performance due to reliance on prior knowledge, while deep learning achieves higher accuracy but requires substantial high-quality training data for precise signal decoding. In this paper, we propose a calibration-free EEG signal decoding framework for fast SSVEP detection. Our framework integrates Inter-Trial Remixing & Context-Aware Distribution Alignment data augmentation for EEG signals and employs a compact architecture of small fully connected layers, effectively addressing the challenge of limited EEG data availability. Additionally, we propose an Adaptive Spectrum Denoise Module that operates in the frequency domain based on global features, requiring only linear complexity to reduce noise in EEG data and improve data quality. For calibration-free classification experiments on short EEG signals from three public datasets, our framework demonstrates statistically significant accuracy advantages(p<0.05) over existing methods in the majority of cases, while requiring at least 52.7% fewer parameters and 29.9% less inference time. By eliminating the need for user-specific calibration, this advancement significantly enhances the usability of BCI systems, accelerating their commercialization and widespread adoption in real-world applications.

cs.HC↗

arXiv2025

Fractional balanced chromatic number of signed subcubic graphs

A signed graph is a pair $(G,σ)$, where $G$ is a graph and $σ: E(G)\rightarrow \{-, +\}$, called signature, is an assignment of signs to the edges. Given a signed graph $(G,σ)$ with no negative loops, a balanced $(p,q)$-coloring of $(G,σ)$ is an assignment $f$ of $q$ colors to each vertex from a pool of $p$ colors such that each color class induces a balanced subgraph, i.e., no negative cycles. Let $(K_4,-)$ be the signed graph on $K_4$ with all edges being negative. In this work, we show that every signed (simple) subcubic graph admits a balanced $(5,3)$-coloring except for $(K_4,-)$ and signed graphs switching equivalent to it. For this particular signed graph the best balanced colorings are $(2p,p)$-colorings.

math.CO↗

arXiv2025

Realizing degree sequences with $\mathcal S_3$-connected graphs

A graph $G$ is $\mathcal S_3$-connected if, for any mapping $β: V (G) \mapsto {\mathbb Z}_3$ with $\sum_{v\in V(G)} β(v)\equiv 0\pmod3$, there exists a strongly connected orientation $D$ satisfying $d^{+}_D(v)-d^{-}_D(v)\equiv β(v)\pmod{3}$ for any $v \in V(G)$. It is known that $\mathcal S_3$-connected graphs are contractible configurations for the property of flow index strictly less than three. In this paper, we provide a complete characterization of graphic sequences that have an $\mathcal{S}_{3}$-connected realization: A graphic sequence $π=(d_1,\, \ldots,\, d_n )$ has an $\mathcal S_3$-connected realization if and only if $\min \{d_1,\, \ldots,\, d_n\} \ge 4$ and $\sum^n_{i=1}d_i \ge 6n - 4$. Consequently, every graphic sequence $π=(d_1,\, \ldots,\, d_n )$ with $\min \{d_1,\, \ldots,\, d_n\} \ge 6$ has a realization $G$ with flow index strictly less than three. This supports a conjecture of Li, Thomassen, Wu and Zhang [European J. Combin., 70 (2018) 164-177] that every $6$-edge-connected graph has flow index strictly less than three.

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