Degree-constrained Subgraph Reconfiguration is in P

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.Comment: Full version of the paper published at Mathematical Foundations of Computer Science (MFCS) 201

COLECCIÓN LUIS SUÁREZ GALVÁN [Material gráfico]

Copia digital. Madrid : Ministerio de Educación, Cultura y Deporte. Subdirección General de Coordinación Bibliotecaria, 201

Independent Set Reconfiguration Parameterized by Modular-Width

Independent Set Reconfiguration is one of the most well-studied problems in the setting of combinatorial reconfiguration. It is known that the problem is PSPACE-complete even for graphs of bounded bandwidth. This fact rules out the tractability of parameterizations by most well-studied structural parameters as most of them generalize bandwidth. In this paper, we study the parameterization by modular-width, which is not comparable with bandwidth. We show that the problem parameterized by modular-width is fixed-parameter tractable under all previously studied rules TAR, TJ, and TS. The result under TAR resolves an open problem posed by Bonsma [WG 2014, JGT 2016]