eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-09-06
24:1
24:15
10.4230/LIPIcs.ESA.2019.24
article
Linear Transformations Between Colorings in Chordal Graphs
Bousquet, Nicolas
1
https://orcid.org/0000-0003-0170-0503
Bartier, Valentin
1
Univ. Grenoble Alpes, CNRS, Grenoble INP, G-SCOP, France
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol144-esa2019/LIPIcs.ESA.2019.24/LIPIcs.ESA.2019.24.pdf
graph recoloring
chordal graphs