License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2018.13
URN: urn:nbn:de:0030-drops-94170
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9417/
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Haviv, Ishay

On Minrank and the Lovász Theta Function

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Abstract

Two classical upper bounds on the Shannon capacity of graphs are the theta-function due to Lovász and the minrank parameter due to Haemers. We provide several explicit constructions of n-vertex graphs with a constant theta-function and minrank at least n^delta for a constant delta>0 (over various prime order fields). This implies a limitation on the theta-function-based algorithmic approach to approximating the minrank parameter of graphs. The proofs involve linear spaces of multivariate polynomials and the method of higher incidence matrices.

BibTeX - Entry

@InProceedings{haviv:LIPIcs:2018:9417,
  author =	{Ishay Haviv},
  title =	{{On Minrank and the Lov{\'a}sz Theta Function}},
  booktitle =	{Approximation, Randomization, and Combinatorial  Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
  pages =	{13:1--13:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-085-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{116},
  editor =	{Eric Blais and Klaus Jansen and Jos{\'e} D. P. Rolim and David Steurer},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9417},
  URN =		{urn:nbn:de:0030-drops-94170},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2018.13},
  annote =	{Keywords: Minrank, Theta Function, Shannon capacity, Multivariate polynomials, Higher incidence matrices}
}

Keywords: Minrank, Theta Function, Shannon capacity, Multivariate polynomials, Higher incidence matrices
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)
Issue Date: 2018
Date of publication: 13.08.2018

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