### Abstract

We improve here the expected performance of parallel algorithms for graph coloring. This is achieved through new adaptive techniques that may be useful for the average-case analysis of many graph algorithms. We apply our techniques to: (a) the class G_{n,p} of random graphs. We present a parallel algorithm which colors the graph with a number of colors at most twice its chromatic number and runs in time O(log^{4} n/ log log n) almost surely, for p = Ω((log^{(3)} n)^{2}/ log^{(2)} n). The number of processors used is O(m) where m is the number of edges of the graph. (b) the class of all fc-colorable graphs, uniformly chosen. We present a parallel algorithm which actually constructs the coloring in expected parallel time O(log^{2} n), for constant k, by using O(m) processors on the average. This problem is not known to have a polynomial time algorithm in the worst case.

Original language | English (US) |
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Title of host publication | Graph-Theoretic Concepts in Computer Science - 17th International Workshop, WG 1991, Proceedings |

Editors | Gunther Schmidt, Rudolf Berghammer |

Publisher | Springer Verlag |

Pages | 135-147 |

Number of pages | 13 |

ISBN (Print) | 9783540551218 |

DOIs | |

State | Published - 1992 |

Event | 17th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 1991 - Fischbachau, Germany Duration: Jun 17 1991 → Jun 19 1991 |

### 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 | 570 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 17th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 1991 |
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Country | Germany |

City | Fischbachau |

Period | 6/17/91 → 6/19/91 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Graph-Theoretic Concepts in Computer Science - 17th International Workshop, WG 1991, Proceedings*(pp. 135-147). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 570 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-55121-2_13