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A New Algorithm for On-line Coloring Bipartite Graphs

Broersma, Hajo J. and Capponi, Agostino and Paulusma, Daniël (2008) A New Algorithm for On-line Coloring Bipartite Graphs. SIAM Journal on Discrete Mathematics, 22 (1). pp. 72-91. ISSN 0895-4801. doi:10.1137/060668675.

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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.

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Additional Information:©2008 Society for Industrial and Applied Mathematics. Received by the editors August 24, 2006; accepted for publication (in revised form) July 17, 2007; published electronically February 8, 2008. An extended abstract of some of the results in this paper was presented at the 6th Italian Conference on Algorithms and Complexity 2006 [3]. We thank the anonymous referees for their useful comments on an earlier version of this paper.
Subject Keywords:on-line coloring; bipartite graph; (on-line) competitive
Issue or Number:1
Record Number:CaltechAUTHORS:BROsiamjdm08
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10098
Deposited By: Archive Administrator
Deposited On:13 Apr 2008
Last Modified:08 Nov 2021 21:05

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