Maximal independent sets in caterpillar graphs

doi:10.1016/j.dam.2011.10.024

Discrete Applied Mathematics

Volume 160, Issue 3, February 2012, Pages 259-266

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Abstract

A caterpillar graph is a tree in which the removal of all pendant vertices results in a chordless path. In this work, we determine the number of maximal independent sets (mis) in caterpillar graphs. For a general graph, this problem is $# P — c o m p l e t e$ . We provide a polynomial time algorithm to generate the whole family of mis in a caterpillar graph. We also characterize the independent graph (intersection graph of mis) and the clique graph (intersection graph of cliques) of complete caterpillar graphs.

Keywords

Graph algorithms

Caterpillar graph

Enumeration of maximal independent sets

Intersection graph

Independent graph

Clique graph

Cited by (0)

^☆: Research partially supported by CNPq, Project PROSUL-Proc. $N^{o}$ 490333/04-4.

^☆☆: A preliminary version of this work was presented at $1 9^{t h}$ International Symposium on Mathematical Programming, Brazil, 2006.

Discrete Applied Mathematics

Maximal independent sets in caterpillar graphs☆,☆☆

Abstract

Keywords