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Proceedings Paper

Linear programming bounds for cliques in Paley graphs
Author(s): Mark Magsino; Dustin G. Mixon; Hans Parshall
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Paper Abstract

The Lovász theta number is a semidefinite programming bound on the clique number of (the complement of) a given graph. Given a vertex-transitive graph, every vertex belongs to a maximal clique, and so one can instead apply this semidefinite programming bound to the local graph. In the case of the Paley graph, the local graph is circulant, and so this bound reduces to a linear programming bound, allowing for fast computations. Impressively, the value of this program with Schrijver's nonnegativity constraint rivals the state-of-the-art closed-form bound recently proved by Hanson and Petridis. We conjecture that this linear programming bound improves on the Hanson{Petridis bound in infinitely often, and we derive the dual program to facilitate proving this conjecture.

Paper Details

Date Published: 9 September 2019
PDF: 8 pages
Proc. SPIE 11138, Wavelets and Sparsity XVIII, 111381H (9 September 2019); doi: 10.1117/12.2526801
Show Author Affiliations
Mark Magsino, The Ohio State Univ. (United States)
Dustin G. Mixon, The Ohio State Univ. (United States)
Hans Parshall, The Ohio State Univ. (United States)

Published in SPIE Proceedings Vol. 11138:
Wavelets and Sparsity XVIII
Dimitri Van De Ville; Manos Papadakis; Yue M. Lu, Editor(s)

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