## Abstract

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 language | English |
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Pages (from-to) | 907-916 |

Number of pages | 10 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E90-A |

Issue number | 5 |

DOIs | |

Publication status | Published - 2007 May |

## Keywords

- 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