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- W4287869968 abstract "List k-Coloring (Li k-Col) is the decision problem asking if a given graph admits a proper coloring compatible with a given list assignment to its vertices with colors in {1,2,..,k}. The problem is known to be NP-hard even for k=3 within the class of 3-regular planar bipartite graphs and for k=4 within the class of chordal bipartite graphs. In 2015, Huang, Johnson and Paulusma asked for the complexity of Li 3-Col in the class of chordal bipartite graphs. In this paper we give a partial answer to this question by showing that Li k-Col is polynomial in the class of convex bipartite graphs. We show first that biconvex bipartite graphs admit a multichain ordering, extending the classes of graphs where a polynomial algorithm of Enright, Stewart and Tardos (2014) can be applied to the problem. We provide a dynamic programming algorithm to solve the Li k-Col in the calss of convex bipartite graphs. Finally we show how our algorithm can be modified to solve the more general Li H-Col problem on convex bipartite graphs." @default.
- W4287869968 created "2022-07-26" @default.
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- W4287869968 date "2020-02-07" @default.
- W4287869968 modified "2023-09-24" @default.
- W4287869968 title "On List k-Coloring Convex Bipartite Graphs" @default.
- W4287869968 doi "https://doi.org/10.48550/arxiv.2002.02729" @default.
- W4287869968 hasPublicationYear "2020" @default.
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