Degree-constrained Subgraph Reconfiguration is in P

TL;DR

This paper proves that the reconfiguration problem for degree-constrained subgraphs, which involves transforming one feasible solution into another through incremental edge modifications while maintaining constraints, can be solved in polynomial time.

Contribution

It establishes that the degree-constrained subgraph reconfiguration problem, a generalization of matching reconfiguration, is in P, demonstrating its polynomial-time solvability.

Findings

Reconfiguration problem for degree-constrained subgraphs is in P.

The problem generalizes the matching reconfiguration problem.

Polynomial-time algorithms exist for the reconfiguration process.

Abstract

The degree-constrained subgraph problem asks for a subgraph of a given graph such that the degree of each vertex is within some specified bounds. We study the following reconfiguration variant of this problem: Given two solutions to a degree-constrained subgraph instance, can we transform one solution into the other by adding and removing individual edges, such that each intermediate subgraph satisfies the degree constraints and contains at least a certain minimum number of edges? This problem is a generalization of the matching reconfiguration problem, which is known to be in P. We show that even in the more general setting the reconfiguration problem is in P.