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Coloring Reconfiguration Under Color Swapping

Authors Janosch Fuchs , Rin Saito , Tatsuhiro Suga , Takahiro Suzuki , Yuma Tamura

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LIPIcs.ISAAC.2025.33.pdf
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ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
Keywords
  • Combinatorial reconfiguration
  • graph coloring
  • PSPACE-complete
  • graph algorithm

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Abstract

In the Coloring Reconfiguration problem, we are given two proper k-colorings of a graph and asked to decide whether one can be transformed into the other by repeatedly applying a specified recoloring rule, while maintaining a proper coloring throughout. For this problem, two recoloring rules have been widely studied: single-vertex recoloring and Kempe chain recoloring. In this paper, we introduce a new rule, called color swapping, where two adjacent vertices may exchange their colors, so that the resulting coloring remains proper, and study the computational complexity of the problem under this rule. We first establish a complexity dichotomy with respect to k: the problem is solvable in polynomial time for k ≤ 2, and is PSPACE-complete for k ≥ 3. We further show that the problem remains PSPACE-complete even on restricted graph classes, including bipartite graphs, split graphs, and planar graphs of bounded degree. In contrast, we present polynomial-time algorithms for several graph classes: for paths when k = 3, for split graphs when k is fixed, and for cographs when k is arbitrary.

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Janosch Fuchs, Rin Saito, Tatsuhiro Suga, Takahiro Suzuki, and Yuma Tamura. Coloring Reconfiguration Under Color Swapping. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 33:1-33:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ISAAC.2025.33

Author Details

Janosch Fuchs
  • IT Center, RWTH Aachen University, Germany
Rin Saito
  • Graduate School of Information Sciences, Tohoku University, Japan
Tatsuhiro Suga
  • Graduate School of Information Sciences, Tohoku University, Japan
Takahiro Suzuki
  • Graduate School of Information Sciences, Tohoku University, Japan
Yuma Tamura
  • Graduate School of Information Sciences, Tohoku University, Japan

Funding

  • Saito, Rin: Supported by JST SPRING Grant Number JPMJSP2114.
  • Tamura, Yuma: Supported by JSPS KAKENHI Grant Number JP25K21148.

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