2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68023Dirac proved that any graph with minimum vertex degree $δ$ contains either a cycle of length at least $2δ$ or a Hamilton cycle. Motivated by this result, we characterize those graphs having no cycle longer than $2δ$.4 pagesCombinatorics05C35; 05C38; 05C75text