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Domination problems on P5-free graphs∗

Published online by Cambridge University Press:  12 January 2015

Min Chih Lin  and
Michel J. Mizrahi
Min Chih Lin
Affiliation:
Intendente Güiraldes 2160, C1428EGA Buenos Aires, Buenos Aires Province, Argentina. oscarlin@dc.uba.ar; michel.mizrahi@gmail.com
Michel J. Mizrahi
Affiliation:
Intendente Güiraldes 2160, C1428EGA Buenos Aires, Buenos Aires Province, Argentina. oscarlin@dc.uba.ar; michel.mizrahi@gmail.com
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Abstract

The minimum roman dominating problem (denoted by γR(G), the weight of minimum roman dominating function of graph G) is a variant of the very well known minimum dominating set problem (denoted by γ(G), the cardinality of minimum dominating set of graph G). Both problems remain NP-Complete when restricted to P5-free graph class [A.A. Bertossi, Inf. Process. Lett. 19 (1984) 37–40; E.J. Cockayne, et al. Discret. Math. 278 (2004) 11–22]. In this paper we study both problems restricted to some subclasses of P5-free graphs. We describe robust algorithms that solve both problems restricted to (P5,(s,t)-net)-free graphs in polynomial time. This result generalizes previous works for both problems, and improves existing algorithms when restricted to certain families such as (P5,bull)-free graphs. It turns out that the same approach also serves to solve problems for general graphs in polynomial time whenever γ(G) and γR(G) are fixed (more efficiently than naive algorithms). Moreover, the algorithms described are extremely simple which makes them useful for practical purposes, and as we show in the last section it allows to simplify algorithms for significant classes such as cographs.

Keywords

Algorithmsdominating setroman dominating functionP5-free graphs
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 48 , Issue 5 , December 2014 , pp. 541 - 549
Copyright
© EDP Sciences 2015

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