### Abstract

Original language | Undefined |
---|---|

Article number | 10.1137/060668675 |

Pages (from-to) | 72-91 |

Number of pages | 20 |

Journal | SIAM journal on discrete mathematics |

Volume | 22 |

Issue number | WoTUG-31/1 |

DOIs | |

Publication status | Published - Feb 2008 |

### Keywords

- IR-62553
- EWI-14147
- METIS-254918

### Cite this

*SIAM journal on discrete mathematics*,

*22*(WoTUG-31/1), 72-91. [10.1137/060668675]. https://doi.org/10.1137/060668675

}

*SIAM journal on discrete mathematics*, vol. 22, no. WoTUG-31/1, 10.1137/060668675, pp. 72-91. https://doi.org/10.1137/060668675

**A new algorithm for on-line coloring bipartite graphs.** / Broersma, Haitze J.; Capponi, A.; Paulusma, Daniël.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - A new algorithm for on-line coloring bipartite graphs

AU - Broersma, Haitze J.

AU - Capponi, A.

AU - Paulusma, Daniël

N1 - 10.1137/060668675

PY - 2008/2

Y1 - 2008/2

N2 - We first show that for any bipartite graph $H$ with at most five vertices there exists an on-line competitive algorithm for the class of $H$-free bipartite graphs. We then analyze the performance of an on-line algorithm for coloring bipartite graphs on various subfamilies. The algorithm yields new upper bounds for the on-line chromatic number of bipartite graphs. We prove that the algorithm is on-line competitive for $P_7$-free bipartite graphs, i.e., that do not contain an induced path on seven vertices. The number of colors used by the on-line algorithm for $P_6$-free and $P_7$-free bipartite graphs is, respectively, bounded by roughly twice and 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 depending only on the chromatic number.

AB - We first show that for any bipartite graph $H$ with at most five vertices there exists an on-line competitive algorithm for the class of $H$-free bipartite graphs. We then analyze the performance of an on-line algorithm for coloring bipartite graphs on various subfamilies. The algorithm yields new upper bounds for the on-line chromatic number of bipartite graphs. We prove that the algorithm is on-line competitive for $P_7$-free bipartite graphs, i.e., that do not contain an induced path on seven vertices. The number of colors used by the on-line algorithm for $P_6$-free and $P_7$-free bipartite graphs is, respectively, bounded by roughly twice and 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 depending only on the chromatic number.

KW - IR-62553

KW - EWI-14147

KW - METIS-254918

U2 - 10.1137/060668675

DO - 10.1137/060668675

M3 - Article

VL - 22

SP - 72

EP - 91

JO - SIAM journal on discrete mathematics

JF - SIAM journal on discrete mathematics

SN - 0895-4801

IS - WoTUG-31/1

M1 - 10.1137/060668675

ER -