Zimu Xiang

activity

20192026

collaborators

12 papers

math.CO2026

List coloring $C_{3}$ -free planar graphs with a sparse matching of restricted lists

Stephen G. Hartke, Yupei Li, Joseph Pappe +3

A graph $G$ is $k$ -choosable if it has a proper coloring for every $k$ -list assignment. While every $C_{3}$ -free planar graph is $4$ -choosable, some of them are not $3$ -choosable, as…

math.CO2026

DP vertex-arboricity of sparse graphs

Peter Bradshaw, Alexandr Kostochka, Zimu Xiang

The vertex arboricity $va (G)$ of a multigraph $G$ is the minimum number $k$ for which $V (G)$ can be partitioned into $k$ subsets, each of which induces an acyclic subgraph…

math.CO2026

An introduction to equitable DP coloring of graphs

H. A. Kierstead, Alexandr Kostochka, Zimu Xiang

A proper $k$ -coloring of vertices of an $n$ -vertex graph is equitable if the size of every color class is $⌊ n / k ⌋$ or $⌈ n / k ⌉$ . An extension of it to list col…

math.CO2025

On Relative Ordered Turán Density

Dylan King, Bernard Lidický, Minghui Ouyang +3

For an ordered graph $F$ , denote the Turán density by $π (F)$ . The relative Turán density, denoted by $ρ (F)$ , is the supremum over $α \in [0, 1]$ such that every ordered graph $G$ …

math.CO2025

On the Turánability and tileability of oriented graphs

Igor Araujo, Zimu Xiang

An oriented graph $H$ is Turánable (resp. tileable) if there exist $n_{0} \in N$ such that every semi-regular near-tournament on $n \geq n_{0}$ vertices contains a copy of $H$ …

math.CO2025

Results and Problems on Equitable Coloring of Graphs

H. A. Kierstead, Alexandr Kostochka, Zimu Xiang

A proper coloring of vertices of a graph is equitable if the sizes of any two color classes differ by at most 1. Such colorings have many applications and are interesting by themse…

math.CO2024

Equitable list coloring of sparse graphs

H. A. Kierstead, Alexandr Kostochka, Zimu Xiang

A proper vertex coloring of a graph is equitable if the sizes of all color classes differ by at most $1$ . For a list assignment $L$ of $k$ colors to each vertex of an $n$ -vertex gr…

math.CO2023

Equitable list coloring of planar graphs with given maximum degree

H. A. Kierstead, Alexandr Kostochka, Zimu Xiang

If $L$ is a list assignment of $r$ colors to each vertex of an $n$ -vertex graph $G$ , then an equitable $L$ -coloring of $G$ is a proper coloring of vertices of $G$ from their lists…

math.CO2023

Equitable coloring of planar graphs with maximum degree at least eight

Alexandr Kostochka, Duo Lin, Zimu Xiang

The Chen-Lih-Wu Conjecture states that each connected graph with maximum degree $Δ \geq 3$ that is not the complete graph $K_{Δ + 1}$ or the complete bipartite graph $K_{Δ, Δ}$ admits…

math.CO2023

Tiling edge-ordered graphs with monotone paths and other structures

Igor Araujo, Simón Piga, Andrew Treglown +1

Given graphs $F$ and $G$ , a perfect $F$ -tiling in $G$ is a collection of vertex-disjoint copies of $F$ in $G$ that together cover all the vertices in $G$ . The study of the minimum…

math.CO2022

Sharp lower bounds for the number of maximum matchings in bipartite multigraphs

Alexandr V. Kostochka, Douglas B. West, Zimu Xiang

We study the minimum number of maximum matchings in a bipartite multigraph G with parts $X$ and $Y$ under various conditions, refining the well-known lower bound due to M. Hall. Wh…

math.NT2019

Higher Order Fibonacci Sequences from Generalized Schreier sets

Hung Viet Chu, Steven J. Miller, Zimu Xiang

A Schreier set $S$ is a subset of the natural numbers with $min S \geq ∣ S ∣$ . It has been known that the sequence $(a_{1, n})$ , where $$a_{1,n}\ :=\ |\{S\subseteq \mathbb{N}\,:\,\max…

List coloring C3​-free planar graphs with a sparse matching of restricted lists

DP vertex-arboricity of sparse graphs

An introduction to equitable DP coloring of graphs

On Relative Ordered Turán Density

On the Turánability and tileability of oriented graphs

Results and Problems on Equitable Coloring of Graphs

Equitable list coloring of sparse graphs

Equitable list coloring of planar graphs with given maximum degree

Equitable coloring of planar graphs with maximum degree at least eight

Tiling edge-ordered graphs with monotone paths and other structures

Sharp lower bounds for the number of maximum matchings in bipartite multigraphs

Higher Order Fibonacci Sequences from Generalized Schreier sets

List coloring $C_{3}$ -free planar graphs with a sparse matching of restricted lists