Yan Cao

activity

20172021

most citedAn improvement to the vertex-splitting conjecture

1 citations · 1 across the 5 of their papers we have counts for

collaborators

7 papers

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…

math.CO2020

Overfullness of critical class 2 graphs with a small core degree

Yan Cao, Guantao Chen, Songling Shan

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

math.CO2020

$Δ$ -critical graphs with a vertex of degree 2

Yan Cao, Guantao Chen, Songling Shan

Let $G$ be a simple graph with maximum degree $Δ$ . A classic result of Vizing shows that $χ^{'} (G)$ , the chromatic index of $G$ , is either $Δ$ or $Δ + 1$ . We say $G$ is of \emph{Class 1…

math.CO2020

Proof of the Core Conjecture of Hilton and Zhao

Yan Cao, Guantao Chen, Guangming Jing +1

Let $G$ be a simple graph with maximum degree $Δ$ . We call $G$ \emph{overfull} if $∣ E (G) ∣ > Δ ⌊ ∣ V (G) ∣/2 ⌋$ . The \emph{core} of $G$ , denoted $G_{Δ}$ , is the subgraph of $G$ i…

math.CO2019

On Gupta's Co-density Conjecture

Yan Cao, Guantao Chen, Guoli Ding +2

Let $G = (V, E)$ be a multigraph. The {\em cover index} $ξ (G)$ of $G$ is the greatest integer $k$ for which there is a coloring of $E$ with $k$ colors such that each vertex of $G$ is…

math.CO2018

Independence number of edge-chromatic critical graphs

Yan Cao, Guantao Chen, Guangming Jing +1

Let $G$ be a simple graph with maximum degree $Δ (G)$ and chromatic index $χ^{'} (G)$ . A classic result of Vizing indicates that either $χ^{'} (G) = Δ (G)$ or $χ^{'} (G) = Δ (G) + 1$ . The graph $G$ i…

An improvement to the vertex-splitting conjecture

Overfullness of critical class 2 graphs with a small core degree

Δ-critical graphs with a vertex of degree 2

Proof of the Core Conjecture of Hilton and Zhao

On Gupta's Co-density Conjecture

Independence number of edge-chromatic critical graphs

$Δ$ -critical graphs with a vertex of degree 2