Using split composition to extend distance-hereditary graphs in a generative way

Authors:
Serafino Cicerone
Affiliations:
Department of Electrical & Information Engineering, University of L'Aquila, L'Aquila, Italy
Venue:
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Year:
2011

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Abstract

In this paper we introduce a new graph class denoted as Gen(*; P3,C3,C5). It contains all graphs that can be generated via split composition by using paths P3 and cycles C3 and C5 as components. This new graph class extends the well known class of distance-hereditary graphs, which corresponds to Gen(*; P3,C3). For the new class we provide efficient algorithms for several basic combinatorial problems: recognition, stretch number, stability number, clique number, domination number, chromatic number, graph isomorphism, and clique width.