Xuding Zhu

activity

20232026

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14 papers · 1 filter

math.CO2026

Tighter Bounds on the Degree-Truncated Choice Number of Planar Graphs

Huijuan Xu, Huan Zhou, Jialu Zhu +1

Assume $G$ is a graph and $k$ is a positive integer. Let $f : V (G) \to N$ be defined as $f (v) = min {k, d_{G} (v)}$ . If $G$ is $f$ -choosable, then we say $G$ is degree-truncated…

math.CO2025

Planar graphs without cycles of length 4 or 5 are $(7 m : 2 m)$ -DP-colorable

Xiaoyan Xu, Xuding Zhu

It was conjectured by Steinberg in 1976 that planar graphs without cycles of length 4 or 5 are 3-colorable. This conjecture attracted a substantial amount of attention and was fina…

math.CO2025

On Alon-Tarsi orientations of sparse graphs

Eun-Kyung Cho, Ilkyoo Choi, Boram Park +1

Assume $G$ is a graph, $(v_{1}, \dots, v_{k})$ is a sequence of distinct vertices of $G$ , and $(a_{1}, \dots, a_{k})$ is an integer sequence with $a_{i} \in {1, 2}$ . We say $G$ is \emph{$(a_1…

math.CO2025

Degree-truncated choosability of graphs

Huan Zhou, Jialu Zhu, Xuding Zhu

A graph $G$ is called degree-truncated $k$ -choosable if for every list assignment $L$ with $∣ L (v) ∣ \geq min {d_{G} (v), k}$ for each vertex $v$ , $G$ is $L$ -colourable. Richter asked…

math.CO2025

Indicated list colouring game on graphs

Yangyan Gu, Yiting Jiang, Huan Zhou +2

Given a graph $G$ and a list assignment $L$ for $G$ , the indicated $L$ -colouring game on $G$ is played by two players: Ann and Ben. In each round, Ann chooses an uncoloured vertex…

math.CO2024

Truncated degree AT-orientations of outerplanar graphs

Chenglong Deng, Xuding Zhu

An AT-orientation of a graph $G$ is an orientation $D$ of $G$ such that the number of even Eulerian sub-digraphs and the number of odd Eulerian sub-digraphs of $D$ are distinct. Gi…

math.CO2024

Planar graphs having no cycle of length $4$ , $6$ or $8$ are DP-3-colorable

Ligang Jin, Yingli Kang, Xuding Zhu

The concept of DP-coloring of graphs was introduced by Dvořák and Postle, and was used to prove that planar graphs without cycles of length from $4$ to $8$ are $3$ -choosable. In th…

math.CO2024

Colouring signed analogues of Kneser, Schrijver, and Borsuk graphs

Luis Kuffner, Reza Naserasr, Lujia Wang +3

The Kneser signed graph $\KS(n,k)$, $k \leq n$ , is the graph whose vertices are signed $k$ -subsets of $[n]$ (i.e. $k$ -subsets $S$ of ${\pm 1, \pm 2, \dots, \pm n}$ such that $S\…

math.CO2024

Odd 4-coloring of outerplanar graphs

Masaki Kashima, Xuding Zhu

A proper $k$ -coloring of $G$ is called an odd coloring of $G$ if for every vertex $v$ , there is a color that appears at an odd number of neighbors of $v$ . This concept was introduc…

math.CO2024

Degree-truncated choosability of planar graphs

Yiting Jiang, Huijuan Xu, Xinbo Xu +1

Assume $G$ is a graph and $k$ is a positive integer. Let $f : V (G) \to N$ be defined as $f (v) = min {k, d_{G} (v)}$ . If $G$ is $f$ -choosable, then we say $G$ is degree-truncated…

math.CO2023

Disjoint list-colorings for planar graphs

Stijn Cambie, Wouter Cames van Batenburg, Xuding Zhu

One of Thomassen's classical results is that every planar graph of girth at least $5$ is 3-choosable. One can wonder if for a planar graph $G$ of girth sufficiently large and a $3$ …

math.CO2023

Truncated degree DP-colourability of $K_{2, 4}$ -minor free graphs

On-Hei Solomon Lo, Cheng Wang, Huan Zhou +1

Assume $G$ is a graph and $k$ is a positive integer. Let $f$ from $V (G)$ to $N$ be defined as $f (v)$ is the minimum of $k$ and $d (v)$ . If $G$ is $f$ -DP-colourable (respectively, $…

math.CO2023

Sparse critical graphs for defective $(1, 3)$ -coloring

Alexandr Kostochka, Jingwei Xu, Xuding Zhu

A graph $G$ is $(1, 3)$ -colorable if its vertices can be partitioned into subsets $V_{1}$ and $V_{2}$ so that every vertex in $G [V_{1}]$ has degree at most $1$ and every vertex in $G[V_2]…

math.CO2023

Weak degeneracy of planar graphs and locally planar graphs

Ming Han, Tao Wang, Jianglin Wu +2

Weak degeneracy is a variation of degeneracy which shares many nice properties of degeneracy. In particular, if a graph $G$ is weakly $d$ -degenerate, then for any $(d + 1)$ -list as…

Tighter Bounds on the Degree-Truncated Choice Number of Planar Graphs

Planar graphs without cycles of length 4 or 5 are (7m:2m)-DP-colorable

On Alon-Tarsi orientations of sparse graphs

Degree-truncated choosability of graphs

Indicated list colouring game on graphs

Truncated degree AT-orientations of outerplanar graphs

Planar graphs having no cycle of length 4, 6 or 8 are DP-3-colorable

Colouring signed analogues of Kneser, Schrijver, and Borsuk graphs

Odd 4-coloring of outerplanar graphs

Degree-truncated choosability of planar graphs

Disjoint list-colorings for planar graphs

Truncated degree DP-colourability of K2,4​-minor free graphs

Sparse critical graphs for defective (1,3)-coloring

Weak degeneracy of planar graphs and locally planar graphs

Planar graphs without cycles of length 4 or 5 are $(7 m : 2 m)$ -DP-colorable

Planar graphs having no cycle of length $4$ , $6$ or $8$ are DP-3-colorable

Truncated degree DP-colourability of $K_{2, 4}$ -minor free graphs

Sparse critical graphs for defective $(1, 3)$ -coloring