The Hilton--Zhao Conjecture is True for Graphs with Maximum Degree 4

Daniel W. Cranston, Landon Rabern

A simple graph $G$ is \emph{overfull} if $|E(G)|>\Delta \lfloor |V(G)|/2\rfloor$. By the pigeonhole principle, every overfull graph $G$ has ${\chi }^{\prime }(G)>\Delta$. The \emph{core} of a graph, denoted…