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On Minrank and the Lovász Theta Function

Author Ishay Haviv

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Ishay Haviv
  • School of Computer Science, The Academic College of Tel Aviv-Yaffo, Tel Aviv 61083, Israel

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Ishay Haviv. On Minrank and the Lovász Theta Function. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 13:1-13:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2018.13

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.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Information theory
Keywords
  • Minrank
  • Theta Function
  • Shannon capacity
  • Multivariate polynomials
  • Higher incidence matrices

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