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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2018.55
URN: urn:nbn:de:0030-drops-96372
URL: https://drops.dagstuhl.de/opus/volltexte/2018/9637/
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Kanté, Mamadou M. ; Khoshkhah, Kaveh ; Pourmoradnasseri, Mozhgan

Enumerating Minimal Transversals of Hypergraphs without Small Holes

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LIPIcs-MFCS-2018-55.pdf (0.6 MB)


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.

BibTeX - Entry

@InProceedings{kant_et_al:LIPIcs:2018:9637,
  author =	{Mamadou M. Kant{\'e} and Kaveh Khoshkhah and Mozhgan Pourmoradnasseri},
  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 =	{Igor Potapov and Paul Spirakis and James Worrell},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9637},
  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}
}

Keywords: Triangle-free Hypergraph, Minimal Transversal, Balanced Matrix, Minimal Dominating Set
Seminar: 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)
Issue Date: 2018
Date of publication: 20.08.2018


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