Domination problems on P5-free graphs

• Autores: Lin, Min Chih; Mizrahi, Michel Jonathan
• Año de publicación: 2014
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Algorithms; Dominating Set; Roman Dominating Function; P5-Free Graphs
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

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.
Fil: Lin, Min Chih. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Mizrahi, Michel Jonathan. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina