We call a graph positive if it has a nonnegative homomorphism number into any target graph with real edge weights. The Positive Graphs Conjecture offers a structural characterization: these are exactly the graphs that can be obtained by gluing together two copies of the same graph along an independent set of vertices. In this talk I will discuss our recent results on the Positive Graphs Conjecture.
- Hilbert's seventeenth problem
- homomorphism number
- positive graphs conjecture
- quantum graph
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics