Overfullness of critical class 2 graphs with a small core degree
Yan Cao, Guantao Chen, Songling Shan · arXiv (Cornell University) · 2020
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 $|E(G)|/\lfloor n/2\rfloor > Δ(G)$, and critical if $χ'(H) n/2 +1$. We show that for any critical class 2 graph $G$, if the minimum degree of $G_Δ$ is at most two and $Δ(G) > n/2 +1$, then $G$ is overfull.