### Abstract

The b-chromatic number b(G) of a graph G = (V,E) is the largest integer κ such that G admits a vertex partition into κ independent sets X_{i} (i = 1,. ., κ) such that each X_{i} contains a vertex x_{i} adjacent to at least one vertex of each X_{j}, j ≠ i. We discuss on the tightness of some bounds on b(G) and on the complexity of determining b(G). We also determine the asymptotic behavior of b(G _{n,p}) for the random graph, within the accuracy of a multiplicative factor 2 + o(1) as n→∞.

Original language | English |
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Title of host publication | Graph-Theoretic Concepts in Computer Science - 28th International Workshop, WG 2002, Revised Papers |

Publisher | Springer Verlag |

Pages | 310-320 |

Number of pages | 11 |

ISBN (Print) | 3540003312, 9783540003311 |

Publication status | Published - Jan 1 2002 |

Event | 28th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2002 - Cesky Krumlov, Czech Republic Duration: Jun 13 2002 → Jun 15 2002 |

### 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 | 2573 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 28th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2002 |
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Country | Czech Republic |

City | Cesky Krumlov |

Period | 6/13/02 → 6/15/02 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

Kratochvíl, J., Tuza, Z., & Voigt, M. (2002). On the b-chromatic number of graphs. In

*Graph-Theoretic Concepts in Computer Science - 28th International Workshop, WG 2002, Revised Papers*(pp. 310-320). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2573 LNCS). Springer Verlag.