Jialu Zhu

activity

20192026

most citedArc weighted acyclic orientations and variations of degeneracy of graphs

1 citations · 3 across the 9 of their papers we have counts for

collaborators

9 papers

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

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.CO2023★ 1 cited

Arc weighted acyclic orientations and variations of degeneracy of graphs

Huan Zhou, Jialu Zhu, Xuding Zhu

This paper studies generalizations of the concept of acyclic orientations to arc-weighted orientations. These lead to four types of variations of strict degeneracy of graphs. Some…

math.CO2022

Minimum non-chromatic- $λ$ -choosable graphs

Jialu Zhu, Xuding Zhu

For a multi-set $λ = {k_{1}, k_{2}, \dots, k_{q}}$ of positive integers, let $k_{λ} = \sum_{i = 1}^{q} k_{i}$ . A $λ$ -list assignment of $G$ is a list assignment $L$ of $G$ such that the colour s…

math.CO2022★ 1 cited

Bad list assignments for non- $k$ -choosable $k$ -chromatic graphs with $2 k + 2$ -vertices

Jialu Zhu, Xuding Zhu

It was conjectured by Ohba, and proved by Noel, Reed and Wu that $k$ -chromatic graphs $G$ with $∣ V (G) ∣ \leq 2 k + 1$ are chromatic-choosable. This upper bound on $∣ V (G) ∣$ is tight: if…

math.CO2022★ 1 cited

Minimum non-chromatic-choosable graphs with given chromatic number

Jialu Zhu, Xuding Zhu

A graph $G$ is called chromatic-choosable if $χ (G) = c h (G)$ . A natural problem is to determine the minimum number of vertices in a $k$ -chromatic non- $k$ -choosable graph. It was conje…

math.CO2021

The fractional chromatic number of double cones over graphs

Jialu Zhu, Xuding Zhu

Assume $n, m$ are positive integers and $G$ is a graph. Let $P_{n, m}$ be the graph obtained from the path with vertices ${- m, - (m - 1), \dots, 0, \dots, n}$ by adding a loop at v…

math.CO2019

Chromatic $λ$ -choosable and $λ$ -paintable graphs

Jialu Zhu, Xuding Zhu

Let $ϕ (k)$ be the minimum number of vertices in a non- $k$ -choosable $k$ -chromatic graph. The Ohba conjecture, confirmed by Noel, Reed and Wu, asserts that $ϕ (k) \geq 2 k + 2$ . This bou…

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

Degree-truncated choosability of graphs

Indicated list colouring game on graphs

Arc weighted acyclic orientations and variations of degeneracy of graphs

Minimum non-chromatic-λ-choosable graphs

Bad list assignments for non-k-choosable k-chromatic graphs with 2k+2-vertices

Minimum non-chromatic-choosable graphs with given chromatic number

The fractional chromatic number of double cones over graphs

Chromatic λ-choosable and λ-paintable graphs

Minimum non-chromatic- $λ$ -choosable graphs

Bad list assignments for non- $k$ -choosable $k$ -chromatic graphs with $2 k + 2$ -vertices

Chromatic $λ$ -choosable and $λ$ -paintable graphs