On implicit heavy subgraphs and hamiltonicity of 2–connected graphs

Wei Zheng (1) , Wojciech Wideł (2) , Ligong Wang (1)

1 Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xi’an, Shaanxi 710072
2 EMSEC - EMbedded SEcurity and Cryptography

A 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.

Mots clés: Implicit degree; Implicit o–heavy; Implicit f–heavy; Implicit c–heavy; Hamilton cycle

Domaines: Mathématique discrète [cs.DM]

Wei Zheng, Wojciech Wideł, Ligong Wang. On implicit heavy subgraphs and hamiltonicity of 2–connected graphs. Discussiones Mathematicae Graph Theory, In press. ⟨hal-01867136⟩