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 \(\chi'(G)\) 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, \(\chi'(G) \leq \Delta(G) +1\) and \(\chi”(G) \leq \Delta(G)+2\) if \(\Delta(G) \geq 6\), and \(\chi'(G) = \Delta(G)\) if \(\Delta(G) \geq 8\).