arXiv subjects

Yiqiao Wang

Publications and source records attributed to Yiqiao Wang.

12 recordsLinked to original sources

arXiv2026

Degeneracy bounds, stability, and a sharp gap for $B$-colorings

A $B$-coloring of a graph is a proper edge-coloring in which every $4$-cycle is rainbow, and $q_B(G)$ denotes the minimum number of colors in such a coloring. Let $Δ_2(G)$ denote the maximum number of common neighbors of two distinct vertices of $G$. We prove that, for integers $1\le d\leΔ$, every finite simple $d$-degenerate graph $G$ with $Δ(G)\leΔ$ satisfies $$q_B(G)\le Δ+(d-1)Δ_2(G)\le dΔ.$$ Consequently, $dΔ$ is the exact maximum, with equality precisely for graphs containing $K_{d,Δ}$. More generally, if $q_B(G)\ge dΔ-s$, where $0\le s<Δ$, then $G$ contains $K_{d,Δ-s}$; if also $s<d$, then $G$ has at least $d-s$ vertices of degree $Δ$ with the same open neighborhood. For $Δ\ge3$, we further show that every $K_{3,Δ}$-free 3-degenerate graph satisfies $q_B(G)\le3Δ-2$; the example $K_{3,Δ-1}$ shows that this bound is best possible up to one. For loopless multigraphs, we establish a sharp gap in the possible values of $q_B(G)$. For every integer $Δ\ge3$, every finite loopless multigraph $G$ with $Δ(G)\leΔ$ satisfies $$q_B(G)\leΔ(Δ-1)$$ unless $G$ has a component isomorphic to $K_{Δ,Δ}$, in which case $q_B(G)=Δ^2$. The bound $Δ(Δ-1)$ is attained by both $K_{Δ,Δ-1}$ and $K_{Δ,Δ}-e$. Consequently, among finite loopless multigraphs with maximum degree at most $Δ$, no value of $q_B(G)$ lies strictly between $Δ^2-Δ$ and $Δ^2$.

math.CO↗

arXiv2026

1-Planar graphs without 6-cycles are 6-choosable

A graph is 1-planar if it can be drawn in the plane so that each edge is crossed by at most one other edge. A graph is $k$-degenerate if each of its subgraphs contains a vertex of degree at most $k$. It was known that every 1-planar graph is 8-choosable. In this paper, we show that every 1-planar graph without 6-cycles is 5-degenerate and hence 6-choosable.

math.CO↗

arXiv2026

Feedback-arc robustness in random orientations of pseudorandom triangle-free graphs

For an oriented graph $D$, let $\vecα(D)$ be the maximum order of an induced acyclic subdigraph, $\vecχ(D)$ its dichromatic number, and $\mathrm{fas}(D)$ the minimum number of arcs whose deletion makes $D$ acyclic. We prove that for every fixed $ζ\in (0, 1/2)$, there are triangle-free graphs $G_n$ on $n$ vertices such that a uniformly random orientation $D_n$ satisfies, $$ \left( \frac{1}{2} - ζ\right) e(G_n[U]) < \mathrm{fas}(D_n[U]) \leq \frac{1}{2} e(G_n[U]) $$ with probability at least $1-\exp\!\left[-Ω_ζ\!\left(\sqrt n\,(\log n)^{3/2}\right)\right]$ simultaneously for every vertex set $U$ of size at least $C_ζ\sqrt{n\log n}$. The upper bound is universal, so the feedback-arc ratio can be made arbitrarily close to the largest possible value, uniformly over all sufficiently large induced subdigraphs. In particular, $\vecα(D_n) = O(\sqrt{n \log n})$, and every linear-size induced subdigraph has dichromatic number $Ω(\sqrt{n/\log n})$. This yields $\vecα(n) = Θ(\sqrt{n \log n})$ and $\vec{t}(n) = Θ\left(\sqrt{\frac{n}{\log n}}\right)$, where $\vecα(n)$ and $\vec{t}(n)$ denote, respectively, the minimum of $\vecα(D)$ and the maximum of $\vecχ(D)$ over all oriented triangle-free graphs $D$ of order $n$. This confirms two conjectures of Aboulker, Havet, Pirot, and Schabanel.

math.CO↗

arXiv2026

D-coloring of planar graphs

A proper edge-coloring of a graph $G$ is a D-coloring if every subgraph isomorphic to $K_4-e$ is rainbow. The minimum number of colors in such a coloring is the D-chromatic index $χ'_D(G)$. Wang conjectured that every planar graph of maximum degree $Δ\ge 4$ satisfies $χ'_D(G) \le 9$ for $Δ= 4$, $χ'_D(G) \le 10$ for $Δ= 5$, and $χ'_D(G) \le 2Δ- 1$ for $Δ\ge 6$. We prove that every planar graph $G$ satisfies \[ χ_D'(G) \leq \begin{cases} 9, & Δ(G) \leq 4, \\ 10, & Δ(G) = 5, \\ 2Δ(G) - 1, & Δ(G) \geq 33. \end{cases} \] Each bound is best possible in its stated range. Consequently, Wang's conjecture remains open only for $6 \le Δ\le 32$.

math.CO↗

arXiv2025

Scalable MatMul-free Language Modeling

Large Language Models (LLMs) have fundamentally altered how we approach scaling in machine learning. However, these models pose substantial computational and memory challenges, primarily due to the reliance on matrix multiplication (MatMul) within their attention and feed-forward (FFN) layers. We demonstrate that MatMul operations can be eliminated from LLMs while maintaining strong performance, even at billion-parameter scales. Our MatMul-free models, tested on models up to 2.7B parameters, are comparable to state-of-the-art pre-trained Transformers, and the performance gap narrows as model size increases. Our approach yields significant memory savings: a GPU-efficient implementation reduces memory consumption by up to 61% during training and over 10x during inference. When adapted for a multi-chip neuromorphic system, the model leverages asynchronous processing to achieve 4x higher throughput with 10x less energy than edge GPUs.

cs.CL↗

arXiv2025

The strong chromatic index of 1-planar graphs

The chromatic index $χ'(G)$ of a graph $G$ is the smallest $k$ for which $G$ admits an edge $k$-coloring such that any two adjacent edges have distinct colors. The strong chromatic index $χ'_s(G)$ of $G$ is the smallest $k$ such that $G$ has an edge $k$-coloring with the condition that any two edges at distance at most 2 receive distinct colors. A graph is 1-planar if it can be drawn in the plane so that each edge is crossed by at most one other edge. In this paper, we show that every graph $G$ with maximum average degree $\bar{d}(G)$ has $χ'_{s}(G)\le (2\bar{d}(G)-1)χ'(G)$. As a corollary, we prove that every 1-planar graph $G$ with maximum degree $Δ$ has $χ'_{\rm s}(G)\le 14Δ$, which improves a result, due to Bensmail et al., which says that $χ'_{\rm s}(G)\le 24Δ$ if $Δ\ge 56$.

math.CO↗

arXiv2025

TS-HTFA: Advancing Time Series Forecasting via Hierarchical Text-Free Alignment with Large Language Models

Given the significant potential of large language models (LLMs) in sequence modeling, emerging studies have begun applying them to time-series forecasting. Despite notable progress, existing methods still face two critical challenges: 1) their reliance on large amounts of paired text data, limiting the model applicability, and 2) a substantial modality gap between text and time series, leading to insufficient alignment and suboptimal performance. In this paper, we introduce \textbf{H}ierarchical \textbf{T}ext-\textbf{F}ree \textbf{A}lignment (\textbf{TS-HTFA}), a novel method that leverages hierarchical alignment to fully exploit the representation capacity of LLMs while eliminating the dependence on text data. Specifically, we replace paired text data with adaptive virtual text based on QR decomposition word embeddings and learnable prompt. Furthermore, we establish comprehensive cross-modal alignment at three levels: input, feature, and output. Extensive experiments on multiple time-series benchmarks demonstrate that HTFA achieves state-of-the-art performance, significantly improving prediction accuracy and generalization.

cs.AI↗

arXiv2024

Gated Slot Attention for Efficient Linear-Time Sequence Modeling

Linear attention Transformers and their gated variants, celebrated for enabling parallel training and efficient recurrent inference, still fall short in recall-intensive tasks compared to traditional Transformers and demand significant resources for training from scratch. This paper introduces Gated Slot Attention (GSA), which enhances Attention with Bounded-memory-Control (ABC) by incorporating a gating mechanism inspired by Gated Linear Attention (GLA). Essentially, GSA comprises a two-layer GLA linked via $\operatorname{softmax}$, utilizing context-aware memory reading and adaptive forgetting to improve memory capacity while maintaining compact recurrent state size. This design greatly enhances both training and inference efficiency through GLA's hardware-efficient training algorithm and reduced state size. Additionally, retaining the $\operatorname{softmax}$ operation is particularly beneficial in "finetuning pretrained Transformers to RNNs" (T2R) settings, reducing the need for extensive training from scratch. Extensive experiments confirm GSA's superior performance in scenarios requiring in-context recall and in T2R settings.

cs.CL↗

arXiv2024

A Survey of Spatio-Temporal EEG data Analysis: from Models to Applications

In recent years, the field of electroencephalography (EEG) analysis has witnessed remarkable advancements, driven by the integration of machine learning and artificial intelligence. This survey aims to encapsulate the latest developments, focusing on emerging methods and technologies that are poised to transform our comprehension and interpretation of brain activity. We delve into self-supervised learning methods that enable the robust representation of brain signals, which are fundamental for a variety of downstream applications. We also explore emerging discriminative methods, including graph neural networks (GNN), foundation models, and large language models (LLMs)-based approaches. Furthermore, we examine generative technologies that harness EEG data to produce images or text, offering novel perspectives on brain activity visualization and interpretation. The survey provides an extensive overview of these cutting-edge techniques, their current applications, and the profound implications they hold for future research and clinical practice. The relevant literature and open-source materials have been compiled and are consistently being refreshed at \url{https://github.com/wpf535236337/LLMs4TS}

eess.SP↗

arXiv2023

The saturation number of $C_6$

A graph $G$ is called $C_k$-saturated if $G$ is $C_k$-free but $G+e$ not for any $e\in E(\overline{G})$. The saturation number of $C_k$, denoted $sat(n,C_k)$, is the minimum number of edges in a $C_k$-saturated graph on $n$ vertices. Finding the exact values of $sat(n,C_k)$ has been one of the most intriguing open problems in extremal graph theory. In this paper, we study the saturation number of $C_6$. We prove that ${4n}/{3}-2 \le sat(n,C_6) \le {(4n+1)}/{3}$ for $n\ge9$, which significantly improves the existing lower and upper bounds for $sat(n,C_6)$.

math.CO↗

arXiv2021

On critical graphs for the chromatic edge-stability number

The {\em chromatic edge-stability number} $es_χ(G)$ of a graph $G$ is the minimum number of edges whose removal results in a spanning subgraph with the chromatic number smaller than that of $G$. A graph $G$ is called {\em $(3,2)$-critical} if $χ(G)=3$, $es_χ(G)=2$ and for any edge $e\in E(G)$, $es_χ(G-e)<es_χ(G)$. In this paper, we characterize $(3,2)$-critical graphs which contain at least five odd cycles. This answers a question proposed by Brešar, Klavžar and Movarraei in [Critical graphs for the chromatic edge-stability number, {\it Discrete Math.} {\bf 343}(2020) 111845].

math.CO↗

arXiv2012

A new upper bound on the acyclic chromatic indices of planar graphs

An acyclic edge coloring of a graph $G$ is a proper edge coloring such that no bichromatic cycles are produced. The acyclic chromatic index $a'(G)$ of $G$ is the smallest integer $k$ such that $G$ has an acyclic edge coloring using $k$ colors. It was conjectured that $a'(G)\le Δ+2$ for any simple graph $G$ with maximum degree $Δ$. In this paper, we prove that if $G$ is a planar graph, then $a'(G)\leqΔ+7$. This improves a result by Basavaraju et al. [{\em Acyclic edge-coloring of planar graphs}, SIAM J. Discrete Math., 25 (2011), pp. 463-478], which says that every planar graph $G$ satisfies $a'(G)\leqΔ+12$.

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