Positivstellens\"atze for Quantum Multigraphs
Algebraic Geometry
2013-10-28 v1 Combinatorics
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.
Keywords
Cite
@article{arxiv.1310.6903,
title = {Positivstellens\"atze for Quantum Multigraphs},
author = {Tim Netzer and Andreas Thom},
journal= {arXiv preprint arXiv:1310.6903},
year = {2013}
}