L. Wang, W. Wideł, W. Zheng
On implicit heavy subgraphs and Hamiltonicity of 2-connected graphs
Discussiones Mathematicae Graph Theory
Received 29.05.2017, Revised 20.08.2018, Accepted 29.08.2018, doi: 10.7151/dmgt.2170

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.
implicit degree, implicit o-heavy, implicit f-heavy, implicit c-heavy, Hamilton cycle