Algorithms for Coloring Reconfiguration Under Recolorability Digraphs

Authors Soichiro Fujii , Yuni Iwamasa , Kei Kimura , Akira Suzuki



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Author Details

Soichiro Fujii
  • Research Institute for Mathematical Sciences, Kyoto University, Japan
  • School of Mathematical and Physical Sciences, Macquarie University, Sydney, Australia
Yuni Iwamasa
  • Graduate School of Informatics, Kyoto University, Japan
Kei Kimura
  • Faculty of Information Science and Electrical Engineering, Kyushu University, Fukuoka, Japan
Akira Suzuki
  • Graduate School of Information Sciences, Tohoku University, Sendai, Japan

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Soichiro Fujii, Yuni Iwamasa, Kei Kimura, and Akira Suzuki. Algorithms for Coloring Reconfiguration Under Recolorability Digraphs. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 4:1-4:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.ISAAC.2022.4

Abstract

In the k-Recoloring problem, we are given two (vertex-)colorings of a graph using k colors, and asked to transform one into the other by recoloring only one vertex at a time, while at all times maintaining a proper k-coloring. This problem is known to be solvable in polynomial time if k ≤ 3, and is PSPACE-complete if k ≥ 4. In this paper, we consider a (directed) recolorability constraint on the k colors, which forbids some pairs of colors to be recolored directly. The recolorability constraint is given in terms of a digraph R, whose vertices correspond to the colors and whose arcs represent the pairs of colors that can be recolored directly. We provide algorithms for the problem based on the structure of recolorability constraints R, showing that the problem is solvable in linear time when R is a directed cycle or is in a class of multitrees.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
Keywords
  • combinatorial reconfiguration
  • graph coloring
  • recolorability
  • recoloring

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