Minimal split completions of graphs

Authors:
Pinar Heggernes;Federico Mancini
Affiliations:
Department of Informatics, University of Bergen, Bergen, Norway;Department of Informatics, University of Bergen, Bergen, Norway
Venue:
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Year:
2006

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Abstract

We study the problem of adding edges to a given arbitrary graph so that the resulting graph is a split graph, called a split completion of the input graph. Our purpose is to add an inclusion minimal set of edges to obtain a minimal split completion, which means that no proper subset of the added edges is sufficient to create a split completion. Minimal completions of arbitrary graphs into chordal graphs have been studied previously, and new results have been added continuously. There is an increasing interest in minimal completion problems, and minimal completions of arbitrary graphs into interval graphs have been studied very recently. We extend these previous results to split graphs, and we give a characterization of minimal split completions, along with a linear time algorithm for computing a minimal split completion of an arbitrary input graph. Among our results is a new way of partitioning the vertices of a split graph uniquely into three subsets.