Tales of Hoffman: Three extensions of Hoffmanʹs bound on the graph chromatic number

Hoffmanʹs bound on the chromatic number of a graph states that χ ⩾ 1 − λ 1 / λ n . Here we show that the same bound, or slight modifications of it, hold for several graph parameters related to the chromatic number: the vector coloring number, the ψ-covering number and the λ-clustering number.