Yan Cao

activity

20172025

most citedAn improvement to the vertex-splitting conjecture

1 citations · 1 across the 10 of their papers we have counts for

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13 papers · 1 filter

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.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

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)…

math.CO2021

A note on Goldberg's conjecture on total chromatic numbers

Yan Cao, Guantao Chen, Guangming Jing

Let $G = (V (G), E (G))$ be a multigraph with maximum degree $Δ (G)$ , chromatic index $χ^{'} (G)$ and total chromatic number $χ^{''} (G)$ . The Total Coloring conjecture proposed by Behzad and V…

math.CO2021

The Core Conjecture of Hilton and Zhao II: a Proof

Yan Cao, Guantao Chen, Guangming Jing +1

A simple graph $G$ with maximum degree $Δ$ is overfull if $∣ E (G) ∣ > Δ ⌊ ∣ V (G) ∣/2 ⌋$ . The core of $G$ , denoted $G_{Δ}$ , is the subgraph of $G$ induced by its vertices of degre…

math.CO2021

The overfullness of graphs with small minimum degree and large maximum degree

Yan Cao, Guantao Chen, Guangming Jing +1

Given a simple graph $G$ , denote by $Δ (G)$ , $δ (G)$ , and $χ^{'} (G)$ the maximum degree, the minimum degree, and the chromatic index of $G$ , respectively. We say $G$ is \emph{ $Δ$ -critic…