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math.CO2019
Spectral upper bound on the quantum k-independence number of a graph
Pawel Wocjan, Clive Elphick, Aida Abiad
A well known upper bound for the independence number of a graph , due to Cvetković, is that \begin{equation*} α(G) \le n^0 + \min\{n^+ , n^-\} \end{equation*} where $(n^+…
math.CO2019
Spectral Lower Bounds for the Quantum Chromatic Number of a Graph -- Part II
Pawel Wocjan, Clive Elphick, Parisa Darbari
Hoffman proved that a graph with eigenvalues and chromatic number satisfies: \[ χ\ge 1 + κ\] where is the smallest integer such that \[ μ_1…