Degreeconstrained Subgraph Reconfiguration is in P
Abstract
The degreeconstrained 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 degreeconstrained 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.
 Publication:

arXiv eprints
 Pub Date:
 August 2015
 arXiv:
 arXiv:1508.01372
 Bibcode:
 2015arXiv150801372M
 Keywords:

 Computer Science  Discrete Mathematics;
 Mathematics  Combinatorics;
 68R10 (primary);
 05C70;
 05C40 (secondary);
 F.2.2;
 G.2.2
 EPrint:
 Full version of the paper published at Mathematical Foundations of Computer Science (MFCS) 2015