# A new algorithm for on-line coloring bipartite graphs

Broersma, H.J.
and
Capponi, A.
and
Paulusma, D.
(2008)
*A new algorithm for on-line coloring bipartite graphs.*
SIAM Journal on Discrete Mathematics, 22
(1).
pp. 72-91.
ISSN 0895-4801

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Abstract: | We first show that for any bipartite graph with at most five vertices there exists an on-line competitive algorithm for the class of -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 -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 -free and -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 -free (or -free) bipartite graphs, i.e., for which the number of colors is bounded by any function depending only on the chromatic number. |

Item Type: | Article |

Faculty: | Electrical Engineering, Mathematics and Computer Science (EEMCS) |

Research Group: | |

Link to this item: | http://purl.utwente.nl/publications/62553 |

Official URL: | https://doi.org/10.1137/060668675 |

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Metis ID: 254918