# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

# IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

Rejection Rate (2017-2018): c. 84%

# Discussiones Mathematicae Graph Theory

Article in press

Authors:

L. Wang, W. Wideł, W. Zheng

Title:

On implicit heavy subgraphs and Hamiltonicity of 2-connected graphs

Source:

Discussiones Mathematicae Graph Theory

Received: 2017-05-29, Revised: 2018-08-20, Accepted: 2018-08-29, https://doi.org/10.7151/dmgt.2170

Abstract:

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 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