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oai:drops-oai.dagstuhl.de:11145 2024-03-06T10:47:33Z ddc:004 open_access

Linear Transformations Between Colorings in Chordal Graphs Bousquet, Nicolas Bartier, Valentin graph recoloring chordal graphs Let k and d be such that k >= d+2. Consider two k-colorings of a d-degenerate graph G. Can we transform one into the other by recoloring one vertex at each step while maintaining a proper coloring at any step? Cereceda et al. answered that question in the affirmative, and exhibited a recolouring sequence of exponential length. If k=d+2, we know that there exists graphs for which a quadratic number of recolorings is needed. And when k=2d+2, there always exists a linear transformation. In this paper, we prove that, as long as k >= d+4, there exists a transformation of length at most f(Delta) * n between any pair of k-colorings of chordal graphs (where Delta denotes the maximum degree of the graph). The proof is constructive and provides a linear time algorithm that, given two k-colorings c_1,c_2 computes a linear transformation between c_1 and c_2. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Nicolas Bousquet and Valentin Bartier 2019 Is Part Of LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ESA.2019.24 urn:nbn:de:0030-drops-111459 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2019.24 eng https://creativecommons.org/licenses/by/3.0/legalcode