Reconfiguration of Regular Induced Subgraphs

TL;DR

This paper investigates the complexity of reconfiguring regular induced subgraphs in graphs, focusing on specific graph classes like chordal and bipartite graphs, and compares these results to the well-studied independent set reconfiguration problem.

Contribution

It provides a systematic complexity analysis of regular induced subgraph reconfiguration, revealing new insights and contrasts with independent set reconfiguration on certain graph classes.

Findings

Complexity results for reconfiguration on chordal graphs.

Complexity results for reconfiguration on bipartite graphs.

Contrasts with known independent set reconfiguration results.

Abstract

We study the problem of checking the existence of a step-by-step transformation of $d$-regular induced subgraphs in a graph, where $d \ge 0$ and each step in the transformation must follow a fixed reconfiguration rule. Our problem for $d=0$ is equivalent to \textsc{Independent Set Reconfiguration}, which is one of the most well-studied reconfiguration problems. In this paper, we systematically investigate the complexity of the problem, in particular, on chordal graphs and bipartite graphs. Our results give interesting contrasts to known ones for \textsc{Independent Set Reconfiguration}.