License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2019.24
URN: urn:nbn:de:0030-drops-111459
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11145/
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Bousquet, Nicolas ; Bartier, Valentin

Linear Transformations Between Colorings in Chordal Graphs

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LIPIcs-ESA-2019-24.pdf (0.6 MB)

Abstract

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.

BibTeX - Entry

@InProceedings{bousquet_et_al:LIPIcs:2019:11145,
  author =	{Nicolas Bousquet and Valentin Bartier},
  title =	{{Linear Transformations Between Colorings in Chordal Graphs}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{24:1--24:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Michael A. Bender and Ola Svensson and Grzegorz Herman},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/11145},
  URN =		{urn:nbn:de:0030-drops-111459},
  doi =		{10.4230/LIPIcs.ESA.2019.24},
  annote =	{Keywords: graph recoloring, chordal graphs}
}

Keywords: graph recoloring, chordal graphs
Collection: 27th Annual European Symposium on Algorithms (ESA 2019)
Issue Date: 2019
Date of publication: 06.09.2019

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