A new algorithm for on-line coloring bipartite graphs

Broersma, H.J.; Capponi, A.; Paulusma, D

Abstract

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.

Citation

Broersma, H., Capponi, A., & Paulusma, D. (2008). A new algorithm for on-line coloring bipartite graphs. SIAM Journal on Discrete Mathematics, 22(1), 72-91. https://doi.org/10.1137/060668675

• Journal Article Type: Article
• Publication Date: Feb 1, 2008
• Deposit Date: Oct 6, 2010
• Publicly Available Date: Oct 7, 2010
• Journal: SIAM Journal on Discrete Mathematics
• Print ISSN: 0895-4801
• Electronic ISSN: 1095-7146
• Publisher: Society for Industrial and Applied Mathematics
• Peer Reviewed: Peer Reviewed
• Volume: 22
• Issue: 1
• Pages: 72-91
• DOI: https://doi.org/10.1137/060668675
• Public URL: https://durham-repository.worktribe.com/output/1548355