2013/10/25 by Netzer, Tim, Thom, Andreas
#Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1310.6903
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 Lovász and Szegedy, and we prove several new Positivstellensätze for nonnegativity of quantum multigraphs. We provide new examples and counterexamples.