Shortest Reconfiguration of Colorings Under Kempe Changes

Marthe Bonamy, Marc Heinrich, Takehiro Ito, Yusuke Kobayashi, Haruka Mizuta, Moritz Mühlenthaler, Akira Suzuki, Kunihiro Wasa, Markus Bläser, Christophe Paul
2020 Symposium on Theoretical Aspects of Computer Science  
A k-coloring of a graph maps each vertex of the graph to a color in {1, 2, ..., k}, such that no two adjacent vertices receive the same color. Given a k-coloring of a graph, a Kempe change produces a new k-coloring by swapping the colors in a bicolored connected component. We investigate the complexity of finding the smallest number of Kempe changes needed to transform a given k-coloring into another given k-coloring. We show that this problem admits a polynomial-time dynamic programming
more » ... hm on path graphs, which turns out to be highly non-trivial. Furthermore, the problem is NP-hard even on star graphs and we show that on such graphs it admits a constant-factor approximation algorithm and is fixed-parameter tractable when parameterized by the number k of colors. The hardness result as well as the algorithmic results are based on the notion of a canonical transformation.
doi:10.4230/lipics.stacs.2020.35 dblp:conf/stacs/BonamyHI0MMSW20 fatcat:kfvdu74mnvdehgbogisfrhueea