Paper Info
Title
Independent Set Reconfiguration in Cographs and their Generalizations
Abstract
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 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 it exists). More generally, we show that if G 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 G using disjoint union and complete join operations. Chordal graphs and claw-free graphs are given as examples of such a class G. (C) 2015 Wiley Periodicals, Inc.
Year
DOI
Venue
2016
10.1002/jgt.21992
JOURNAL OF GRAPH THEORY
Keywords
Field
DocType
reconfiguration,graph classes,efficient algorithm,dynamic programming,graph decomposition
Discrete mathematics,Combinatorics,Graph power,Chordal graph,Independent set,Cograph,Clique-width,Pathwidth,Mathematics,Split graph,Maximal independent set
Journal
Volume
Issue
ISSN
83.0
2.0
0364-9024
Citations 
PageRank 
References 
0
0.34
15
Authors
1
Name
Order
Citations
PageRank
Paul Bonsma128720.46