Edge Choosability and Total Choosability of Toroidal Graphs without Intersecting Triangles

Abstract

Two cycles are said to be intersecting if they share at least one common vertex. Let ${\chi }^{\prime }(G)$ and $\chi ”(G)$ denote the list edge chromatic number and list total chromatic number of a graph $G$, respectively.In this paper, we proved that for any toroidal graph G without intersecting triangles, ${\chi }^{\prime }(G)\le \mathrm{\Delta }(G)+1$ and $\chi ”(G)\le \mathrm{\Delta }(G)+2$ if $\mathrm{\Delta }(G)\ge 6$, and ${\chi }^{\prime }(G)=\mathrm{\Delta }(G)$ if $\mathrm{\Delta }(G)\ge 8$.