### Abstract

We present a new on-line algorithm for coloring bipartite graphs. This yields a new upper bound on the on-line chromatic number of bipartite graphs, improving a bound due to Lovasz, Saks and Trotter. The algorithm is on-line competitive on various classes of $H$-free bipartite graphs, in particular $P_6$-free bipartite graphs and $P_7$-free bipartite graphs, i.e., that do not contain an induced path on six, respectively seven vertices. The number of colors used by the on-line algorithm in these particular cases is bounded by roughly twice, respectively roughly eight times the on-line chromatic number. In contrast, it is known that there exists no competitive on-line algorithm to color $P_6$-free (or $P_7$-free) bipartite graphs, i.e., for which the number of colors is bounded by any function only depending on the chromatic number.

Original language | English |
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Title of host publication | Algorithms and Complexity |

Subtitle of host publication | 6th Italian Conference, CIAC 2006, Rome, Italy, May 29-31, 2006. Proceedings |

Editors | Tiziana Calamoneri, Irene Finocchi, Giuseppe F. Italiano |

Place of Publication | Berlin, Heidelberg |

Publisher | Springer |

Pages | 284-295 |

Number of pages | 12 |

ISBN (Electronic) | 978-3-540-34378-3 |

ISBN (Print) | 978-3-540-34375-2 |

DOIs | |

Publication status | Published - 2006 |

Event | 6th Italian Conference on Algorithms and Complexity, CIAC 2006 - Rome, Italy Duration: 29 May 2006 → 31 May 2006 Conference number: 6 |

### Publication series

Name | Lecture Notes in Computer Science |
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Publisher | Springer |

Volume | 3998 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 6th Italian Conference on Algorithms and Complexity, CIAC 2006 |
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Abbreviated title | CIAC |

Country | Italy |

City | Rome |

Period | 29/05/06 → 31/05/06 |

### Keywords

- EWI-8087
- IR-63662
- METIS-238710

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## Cite this

Broersma, H. J., Capponi, A., & Paulusma, D. (2006). On-line coloring of H-free bipartite graphs. In T. Calamoneri, I. Finocchi, & G. F. Italiano (Eds.),

*Algorithms and Complexity: 6th Italian Conference, CIAC 2006, Rome, Italy, May 29-31, 2006. Proceedings*(pp. 284-295). (Lecture Notes in Computer Science; Vol. 3998). Berlin, Heidelberg: Springer. https://doi.org/10.1007/11758471_28