2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/120949We prove that a random cubic graph almost surely is not homomorphic to a cycle of size 7. This implies that there exist cubic graphs of arbitrarily high girth with no homomorphisms to the cycle of size 7.Combinatorics05C80Random cubic graphs are not homomorphic to the cycle of size 7text