Abstract
The existence of an on-line competitive algorithm for coloring bipartite graphs remains a tantalizing open problem. So far there are only partial positive results for bipartite graphs with certain small forbidden graphs as induced subgraphs, in particular for \(P_7\)-free bipartite graphs. We propose a new on-line competitive coloring algorithm for \(P_8\)-free bipartite graphs. Our proof technique improves the result, and shortens the proof, for \(P_7\)-free bipartite graphs.
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