Title

Strongly Chordal and Chordal Bipartite Graphs Are Sandwich Monotone

Document Type

Article

Publication Date

10-2011

Publication Source

Journal of Combinatorial Optimization

Abstract

A graph class is sandwich monotone if, for every pair of its graphs G1=(V,E1) and G2=(V,E2) with E1E2, there is an ordering e1,…,ek of the edges in E2E1 such that G=(V,E1∪{e1,…,ei }) belongs to the class for every i between 1 and k. In this paper we show that strongly chordal graphs and chordal bipartite graphs are sandwich monotone, answering an open question by Bakonyi and Bono (Czechoslov. Math. J. 46:577–583, 1997). So far, very few classes have been proved to be sandwich monotone, and the most famous of these are chordal graphs. Sandwich monotonicity of a graph class implies that minimal completions of arbitrary graphs into that class can be recognized and computed in polynomial time. For minimal completions into strongly chordal or chordal bipartite graphs no polynomial-time algorithm has been known. With our results such algorithms follow for both classes. In addition, from our results it follows that all strongly chordal graphs and all chordal bipartite graphs with edge constraints can be listed efficiently.

Inclusive pages

438–456

ISBN/ISSN

1382-6905

Comments

Permission documentation on file.

Publisher

Springer

Volume

22

Issue

3

Peer Reviewed

yes


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