On implicit heavy subgraphs and hamiltonicity of 2–connected graphs

International audienceA graph G of order n is implicit claw–heavy if in every induced copy of K 1,3 in G there are two non–adjacent vertices with sum of their implicit degrees at least n. We study various implicit degree conditions (including, but not limiting to, Ore– and Fan–type conditions) imposing of which on specific induced subgraphs of a 2–connected implicit claw–heavy graph ensures its hamiltonicity. In particular, we improve a recent result of [X. Huang, Implicit degree condition for hamiltonic-ity of 2–heavy graphs, Discrete Appl. Math. 219 (2017) 126–131] and complete the characterizations of pairs of o–heavy and f–heavy sub-graphs for hamiltonicity of 2–connected graphs