On linear and circular structure of (claw, net)-free graphs

Authors:
Andreas Brandstädt;Feodor F. Dragan
Affiliations:
Fachbereich Informatik, Universität Rostock, A. Einstein Str. 21, D-18051 Rostock, Germany;Department of Computer Science, Kent State University, Kent, OH
Venue:
Discrete Applied Mathematics
Year:
2003

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Abstract

We prove that every (claw, net)-free graph contains an induced doubly dominating cycle or a dominating pair. Moreover, using LexBFS we present a linear time algorithm which, for a given (claw, net)-free graph, finds either a dominating pair or an induced doubly dominating cycle. We show also how one can use structural properties of (claw, net)-free graphs to solve efficiently the domination, independent domination, and independent set problems on these graphs.