Reconfiguring spanning and induced subgraphs

TL;DR

This paper systematically analyzes the complexity of reconfiguring subgraphs under various graph properties, clarifying the computational challenges involved.

Contribution

It provides a comprehensive classification of the complexity of subgraph reconfiguration problems across different graph structure properties.

Findings

Reconfiguration problems vary in complexity depending on the property considered.

The paper offers a unified framework for understanding subgraph reconfiguration.

Complexity results are systematically organized for multiple graph properties.

Abstract

Subgraph reconfiguration is a family of problems focusing on the reachability of the solution space in which feasible solutions are subgraphs, represented either as sets of vertices or sets of edges, satisfying a prescribed graph structure property. Although there has been previous work that can be categorized as subgraph reconfiguration, most of the related results appear under the name of the property under consideration; for example, independent set, clique, and matching. In this paper, we systematically clarify the complexity status of subgraph reconfiguration with respect to graph structure properties.