2026-04-13T02:28:37Zhttps://recercat.cat/oai/requestoai:recercat.cat:2117/3411442026-02-02T09:09:14Zcom_2072_1033col_2072_452950
RECERCAT
author
Díaz Cort, Josep
author
Yasar Diner, Oznur
author
Serna Iglesias, María José
author
Serra Albó, Oriol
2020
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 class 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.J. Díaz and M. Serna are partially supported by funds from MINECO and EU FEDER under grant TIN 2017-86727-C2-1-R AGAUR project ALBCOM 2017- SGR-786. O. Y. Diner is partially supported by the Scientific and Technological Research Council Tubitak under project BIDEB 2219-1059B191802095 and by Kadir Has University under project 2018-BAP-08. O. Serra is supported by the Spanish Ministry of Science under project MTM2017-82166-P.Peer ReviewedPostprint (author's final draft)
Open Access
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
Graph theory
List coloring
Convex bipartite
Biconvex bipartite graphs
Grafs, Teoria de
On list k-coloring convex bipartite graphs
Conference report