Sufficient Condition and Algorithm for List Total Colorings of Series-Parallel Graphs

Yuki MATSUO
Xiao ZHOU
Takao NISHIZEKI

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E90-A    No.5    pp.907-916
Publication Date: 2007/05/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e90-a.5.907
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
Category: 
Keyword: 
algorithm,  total coloring,  list total coloring,  series-parallel graph,  

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Summary: 
A total coloring of a graph G is a coloring of all elements of G, i.e. vertices and edges, such that no two adjacent or incident elements receive the same color. Let L(x) be a set of colors assigned to each element x of G. Then a list total coloring of G is a total coloring such that each element x receives a color contained in L(x). The list total coloring problem asks whether G has a list total coloring for given L. In this paper, we give a sufficient condition for a series-parallel graph to have a list total coloring, and we present a linear-time algorithm to find a list total coloring of a given series-parallel graph G if G and L satisfy the sufficient condition.

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