### Abstract

A total coloring of a graph G is a coloring of all elements of G, i.e. vertices and edges, in such a way that no two adjacent or incident elements receive the same color. A graph G is s-degenerated for a positive integer s if G can be reduced to a trivial graph by successive removal of vertices with degree ≤ s. We prove that an s-degenerated graph G has a total coloring with δ + 1 colors if the maximum degree δ of G is su-ciently large, say δ ≥ 4s+3. Our proof yields an eficient algorithm to find such a total coloring. We also give a linear-time algorithm to find a total coloring of a graph G with the minimum number of colors if G is a partial k-tree, i.e. the tree-width of G is bounded by a fixed integer k.

Original language | English |
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Title of host publication | Automata, Languages and Programming - 28th International Colloquium, ICALP 2001, Proceedings |

Editors | Fernando Orejas, Paul G. Spirakis, Jan van Leeuwen |

Publisher | Springer Verlag |

Pages | 506-517 |

Number of pages | 12 |

ISBN (Print) | 3540422870, 9783540422877 |

DOIs | |

Publication status | Published - 2001 Jan 1 |

Event | 28th International Colloquium on Automata, Languages and Programming, ICALP 2001 - Crete, Greece Duration: 2001 Jul 8 → 2001 Jul 12 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 2076 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 28th International Colloquium on Automata, Languages and Programming, ICALP 2001 |
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Country | Greece |

City | Crete |

Period | 01/7/8 → 01/7/12 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Automata, Languages and Programming - 28th International Colloquium, ICALP 2001, Proceedings*(pp. 506-517). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2076 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-48224-5_42