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://drops.dagstuhl.de/opus/volltexte/2019/11145/
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### Linear Transformations Between Colorings in Chordal Graphs

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### 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},