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Strongly chordal and chordal bipartite graphs are sandwich monotone

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Abstract

A graph class is sandwich monotone if, for every pair of its graphs G 1=(V,E 1) and G 2=(V,E 2) with E 1⊂E 2, there is an ordering e 1,…,e k of the edges in E 2∖E 1 such that G=(V,E 1∪{e 1,…,e i }) 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.

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Authors and Affiliations

  1. Department of Informatics, University of Bergen, 5020, Bergen, Norway

    Pinar Heggernes & Federico Mancini

  2. Department of Mathematics, University of Ioannina, 45110, Ioannina, Greece

    Charis Papadopoulos

  3. Department of Computer Science, University of Dayton, Dayton, OH, 45469, USA

    R. Sritharan

Authors
  1. Pinar Heggernes
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  2. Federico Mancini
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  3. Charis Papadopoulos
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  4. R. Sritharan
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Corresponding author

Correspondence to Charis Papadopoulos.

Additional information

This work is supported by the Research Council of Norway and National Security Agency, USA.

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Heggernes, P., Mancini, F., Papadopoulos, C. et al. Strongly chordal and chordal bipartite graphs are sandwich monotone. J Comb Optim 22, 438–456 (2011). https://doi.org/10.1007/s10878-010-9322-x

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