FPT algorithms for domination in biclique-free graphs

Authors:
Jan Arne Telle;Yngve Villanger
Affiliations:
Department of Informatics, University of Bergen, Norway;Department of Informatics, University of Bergen, Norway
Venue:
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Year:
2012

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Abstract

A class of graphs is said to be biclique-free if there is an integer t such that no graph in the class contains Kt,t as a subgraph. Large families of graph classes, such as any nowhere dense class of graphs or d-degenerate graphs, are biclique-free. We show that various domination problems are fixed-parameter tractable on biclique-free classes of graphs, when parameterizing by both solution size and t. In particular, the problems k-Dominating Set, Connectedk-Dominating Set, Independentk-Dominating Set and Minimum Weightk-Dominating Set are shown to be FPT, when parameterized by t+k, on graphs not containing Kt,t as a subgraph. With the exception of Connectedk-Dominating Set all described algorithms are trivially linear in the size of the input graph.