Chromatic numbers, Sabidussi's Theorem and Hedetniemi's conjecture for non-commutative graphs

摘要

Non-commutative graph theory is an operator space generalization of graph theory. Well known graph parameters such as the independence number and Lovasz theta function were first generalized to this setting by Duan, Severini, and Winter [1]. In [10], Stahlke introduces a generalization of the chromatic number of a graph and obtains a Lovasz sandwich inequality for certain operator spaces.