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DOI: 10.4230/LIPIcs.MFCS.2018.55

Enumerating Minimal Transversals of Hypergraphs without Small Holes

Authors: Mamadou M. Kanté, Kaveh Khoshkhah, and Mozhgan Pourmoradnasseri

Published in: LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)

Abstract

We give a polynomial delay algorithm for enumerating the minimal transversals of hypergraphs without induced cycles of length 3 and 4. As a corollary, we can enumerate, with polynomial delay, the vertices of any polyhedron P(A,1)={x in R^n | Ax >= 1, x >= 0}, when A is a balanced matrix that does not contain as a submatrix the incidence matrix of a cycle of length 4. Other consequences are a polynomial delay algorithm for enumerating the minimal dominating sets of graphs of girth at least 9 and an incremental delay algorithm for enumerating all the minimal dominating sets of a bipartite graph without induced 6 and 8-cycles.

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Mamadou M. Kanté, Kaveh Khoshkhah, and Mozhgan Pourmoradnasseri. Enumerating Minimal Transversals of Hypergraphs without Small Holes. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 55:1-55:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{kante_et_al:LIPIcs.MFCS.2018.55,
  author =	{Kant\'{e}, Mamadou M. and Khoshkhah, Kaveh and Pourmoradnasseri, Mozhgan},
  title =	{{Enumerating Minimal Transversals of Hypergraphs without Small Holes}},
  booktitle =	{43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
  pages =	{55:1--55:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Potapov, Igor and Spirakis, Paul and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.55},
  URN =		{urn:nbn:de:0030-drops-96372},
  doi =		{10.4230/LIPIcs.MFCS.2018.55},
  annote =	{Keywords: Triangle-free Hypergraph, Minimal Transversal, Balanced Matrix, Minimal Dominating Set}
}

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Enumerating Minimal Transversals of Hypergraphs without Small Holes

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