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Positivstellensätze for Quantum Multigraphs

Published 25 Oct 2013 in math.AG and math.CO | (1310.6903v1)

Abstract: Studying inequalities between subgraph- or homomorphism-densities is an important topic in graph theory. Sums of squares techniques have proven useful in dealing with such questions. Using an approach from real algebraic geometry, we strengthen a Positivstellensatz for simple quantum graphs by Lov\'asz and Szegedy, and we prove several new Positivstellens\"atze for nonnegativity of quantum multigraphs. We provide new examples and counterexamples.

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