Year: 2014
Type: preprint
Abstract: Given graphs $X$ and $Y$, we define two conic feasibility programs which we show have a solution over the completely positive cone if and only if there exists a homomorphism from $X$ to $Y$. By varying the cone, we obtain similar characterizations of quantum/entanglement-assisted homomorphisms and three previously studied relaxations of these relations. Motivated by this, we investigate the properties of these "conic homomorphisms" for general (suitable) cones. We also consider two generalized versions of the Lovász theta function, and how they interact with these conic homomorphisms. We prove analogs of several results on classical graph homomorphisms as well as some monotonicity theorems. We also show that one of the generalized theta functions is multiplicative on lexicographic and disjunctive graph products.
Source: arXiv (Cornell University)
Author: Roberson, David E.
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2950034824