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DOI: 10.4230/LIPIcs.MFCS.2020.41
Fractional Covers of Hypergraphs with Bounded Multi-Intersection

Authors: Georg Gottlob, Matthias Lanzinger, Reinhard Pichler, and Igor Razgon

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Abstract
Fractional (hyper-)graph theory is concerned with the specific problems that arise when fractional analogues of otherwise integer-valued (hyper-)graph invariants are considered. The focus of this paper is on fractional edge covers of hypergraphs. Our main technical result generalizes and unifies previous conditions under which the size of the support of fractional edge covers is bounded independently of the size of the hypergraph itself. This allows us to extend previous tractability results for checking if the fractional hypertree width of a given hypergraph is ≤ k for some constant k. We also show how our results translate to fractional vertex covers.
Cite as

Georg Gottlob, Matthias Lanzinger, Reinhard Pichler, and Igor Razgon. Fractional Covers of Hypergraphs with Bounded Multi-Intersection. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 41:1-41:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{gottlob_et_al:LIPIcs.MFCS.2020.41,
  author =	{Gottlob, Georg and Lanzinger, Matthias and Pichler, Reinhard and Razgon, Igor},
  title =	{{Fractional Covers of Hypergraphs with Bounded Multi-Intersection}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{41:1--41:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.41},
  URN =		{urn:nbn:de:0030-drops-127317},
  doi =		{10.4230/LIPIcs.MFCS.2020.41},
  annote =	{Keywords: Fractional graph theory, fractional edge cover, fractional hypertree width, bounded multi-intersection, fractional cover, fractional vertex cover}
}
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