List Coloring Halin Graphs

Abstract

A Halin graph is a plane graph \(H = T \cup C\), where \(T\) is a tree with no vertex of degree two and at least one vertex of degree three or more, and \(C\) is a cycle connecting the pendant vertices of \(T\) in the cyclic order determined by the drawing of \(T\). In this paper we determine the list chromatic number, the list chromatic index, and the list total chromatic number (except when \(\Delta = 3\)) of all Halin graphs, where \(\Delta\) denotes the maximum degree of \(H\).