Geodesic
On Implicit Heavy Subgraphs and Hamiltonicity of 2-Connected Graphs
Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 1, pp. 167-181

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A graph G of order n is implicit claw-heavy if in every induced copy of K1,3 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 Hamiltonicity of 2-heavy graphs, Discrete Appl. Math. 219 (2017) 126–131] and complete the characterizations of pairs of o-heavy and f-heavy subgraphs for Hamiltonicity of 2-connected graphs.
Keywords: implicit degree, implicit o-heavy, implicit f-heavy, implicit c-heavy, Hamilton cycle 
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Zheng, Wei; Wideł, Wojciech; Wang, Ligong. On Implicit Heavy Subgraphs and Hamiltonicity of 2-Connected Graphs. Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 1, pp. 167-181. http://geodesic.mathdoc.fr/item/DMGT_2021_41_1_a10/