2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71804Hofmman's bound on the chromatic number of a graph states that $χ\geq 1 - \frac {λ_1} {λ_n}$. 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.short note - 6 pagesCombinatorics05c15; 05c50text