Triangle-free quantum graphs

2025/09/22 by Weaver, Nik
#Combinatorics (math.CO) #FOS: Mathematics #Operator Algebras (math.OA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2509.17782

Abstract

We introduce notions of being "triangle-free" and "strongly triangle-free" for operator systems in M_n(C) considered as quantum graphs. Several examples and non-examples are discussed. We provide a complete characterization of strongly triangle-free operator systems.

Citations

• Spectral bounds for the quantum chromatic number of quantum graphs
• Connectivity for quantum graphs
• The "quantum" Turan problem for operator systems
• A "quantum" Ramsey theorem for operator systems
• Quantum graphs as quantum relations
• Quantum relations

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