2014/02/07 by Paul Bonsma, Bonsma, Paul · 1 citation
Computer Science · #Advanced Graph Theory Research #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Graph Labeling and Dimension Problems #Optimization and Search Problems
paper · pdf · doi:10.48550/arxiv.1402.1587
openalex publication_date 2014/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the following independent set reconfiguration problem, called TAR-Reachability: given two independent sets I and J of a graph G, both of size at least k, is it possible to transform I into J by adding and removing vertices one-by-one, while maintaining an independent set of size at least k throughout? This problem is known to be PSPACE-hard in general. For the case that G is a cograph (i.e. P4-free graph) on n vertices, we show that it can be solved in time O(n2), and that the length of a shortest reconfiguration sequence from I to J is bounded by 4n-2k, if such a sequence exists. More generally, we show that if X is a graph class for which (i) TAR-Reachability can be solved efficiently, (ii) maximum independent sets can be computed efficiently, and which satisfies a certain additional property, then the problem can be solved efficiently for any graph that can be obtained from a collection of graphs in X using disjoint union and complete join operations. Chordal graphs are given as an example of such a class X.