Chromatic numbers and a Lov\'asz type inequality for non-commutative graphs

Understand

Non-commutative graph theory is an operator space generalization of graph theory.

• Well known graph parameters such as the independence number and Lov\'asz theta function were first generalized to this setting by Duan, Severini, and Winter.
• We introduce two new generalizations of the chromatic number to non-commutative graphs and provide a generalization of the Lov\'asz sandwich inequality.
• In particular, we show the chromatic number of the orthogonal complement of a non-commutative graph is bounded below by its theta number.