Let G be a graph on n vertices. A vertex of G with degree at least n/2 is called a heavy vertex, and a cycle of G which contains all the heavy vertices of G is called a heavy cycle. In this note, we characterize graphs which contain no heavy cycles. For a given graph H, we say that G is H-heavy if every induced subgraph of G isomorphic to H contains two nonadjacent vertices with degree sum at least n. We find all the connected graphs S such that a 2-connected graph G being S-heavy implies any longest cycle of G is a heavy cycle.
@article{bwmeta1.element.doi-10_7151_dmgt_1863,
author = {Binlong Lia and Shenggui Zhang},
title = {Heavy Subgraph Conditions for Longest Cycles to Be Heavy in Graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {36},
year = {2016},
pages = {383-392},
zbl = {1338.05151},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1863}
}
Binlong Lia; Shenggui Zhang. Heavy Subgraph Conditions for Longest Cycles to Be Heavy in Graphs. Discussiones Mathematicae Graph Theory, Tome 36 (2016) pp. 383-392. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1863/