Yan Cao

activity

20172026

most citedProof of the Core Conjecture of Hilton and Zhao

3 citations · 6 across the 16 of their papers we have counts for

collaborators

17 papers

math.CO2026

Decomposing multigraphs into two Class I subgraphs with prescribed maximum degrees

Yonglei Chen, Yan Cao

Let $G$ be a finite loopless multigraph with maximum degree $Δ$ and $χ^{'} (G) = Δ + k$ , where $k \geq 0$ . We prove that for every pair of positive integers $p, q$ satisfying $$p+q=Δ+k\qquad\t…

math.CO2025

Short Brooms in Edge-chromatic Critical Graphs

Yonglei Chen, Yan Cao

This paper studies short brooms in edge-chromatic critical graphs. We prove that for any short broom in a $Δ$ -critical graph, at most one color is missing at more than one vertex.…

math.CO2023

The average degree of edge chromatic critical graphs with maximum degree seven

Yan Cao, Rong Luo, Zhengke Miao +1

In this paper, by developing several new adjacency lemmas about a path on $4$ or $5$ vertices, we show that the average degree of 7-critical graphs is at least 6. It implies Vizing…

math.CO2022

Decomposition of class II graphs into two class I graphs

Yan Cao, Guangming Jing, Rong Luo +3

Mkrtchyan and Steffen [J. Graph Theory, 70 (4), 473--482, 2012] showed that every class II simple graph can be decomposed into a maximum $Δ$ -edge-colorable subgraph and a matching.…

math.CO2022

Overfullness of edge-critical graphs with small minimal core degree

Yan Cao, Guantao Chen, Guangming Jing +1

Let $G$ be a simple graph. Denote by $n$ , $Δ (G)$ and $χ^{'} (G)$ be the order, the maximum degree and the chromatic index of $G$ , respectively. We call $G$ \emph{overfull} if $|E(G)|/…

math.CO2022

Precoloring extension of Vizing's Theorem for multigraphs

Yan Cao, Guantao Chen, Guangming Jing +2

Let $G$ be a graph with maximum degree $Δ (G)$ and maximum multiplicity $μ (G)$ . Vizing and Gupta, independently, proved in the 1960s that the chromatic index of $G$ is at most $Δ(G)…