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Algorithms for Coloring Reconfiguration Under Recolorability Digraphs

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

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Subject Classification

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

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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.

Cite As Get BibTex

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

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

Funding

  • Fujii, Soichiro: Partially supported by JST, ERATO Grant Number JPMJER1603 (HASUO Metamathematics for Systems Design Project) and JSPS Overseas Research Fellowships.
  • Iwamasa, Yuni: Partially supported by JSPS KAKENHI Grant Numbers JP20K23323, JP20H05795, 22K17854, Japan.
  • Kimura, Kei: Partially supported by JSPS KAKENHI Grant Numbers JP19K22841, JP21K17700, Japan.
  • Suzuki, Akira: Partially supported by JSPS KAKENHI Grant Numbers JP18H04091, JP20K11666, JP20H05794, Japan.

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