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

Showing 2021Show all

5 papers · 1 filter

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★ 1 cited

Pseudo-multifan and Lollipop

Yan Cao, Guantao Chen, Guangming Jing +1

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

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…

math.CO2021★ 1 cited

An improvement to the vertex-splitting conjecture

Yan Cao, Guantao Chen, Songling Shan

For a simple graph $G$ , denote by $n$ , $Δ (G)$ , and $χ^{'} (G)$ its order, maximum degree, and chromatic index, respectively. A connected class 2 graph $G$ is edge-chromatic critical if…