Sufficient condition and algorithm for list total colorings of series-parallel graphs

Yuki Matsuo, Xiao Zhou, Takao Nishizeki

Research output: Contribution to journalArticlepeer-review


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 × of G. Then a list total coloring of G is a total coloring such that each element × 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.

Original languageEnglish
Pages (from-to)907-916
Number of pages10
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Issue number5
Publication statusPublished - 2007 May


  • Algorithm
  • List total coloring
  • Series-parallel graph
  • Total coloring

ASJC Scopus subject areas

  • Signal Processing
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering
  • Applied Mathematics


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