Heavy Subgraph Conditions for Longest Cycles to Be Heavy in Graphs

Binlong Lia, and Shenggui Zhang. "Heavy Subgraph Conditions for Longest Cycles to Be Heavy in Graphs." Discussiones Mathematicae Graph Theory 36.2 (2016): 383-392. <http://eudml.org/doc/277124>.

@article{BinlongLia2016,
abstract = {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.},
author = {Binlong Lia, Shenggui Zhang},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {heavy cycles; heavy subgraphs},
language = {eng},
number = {2},
pages = {383-392},
title = {Heavy Subgraph Conditions for Longest Cycles to Be Heavy in Graphs},
url = {http://eudml.org/doc/277124},
volume = {36},
year = {2016},
}

TY - JOUR
AU - Binlong Lia
AU - Shenggui Zhang
TI - Heavy Subgraph Conditions for Longest Cycles to Be Heavy in Graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2016
VL - 36
IS - 2
SP - 383
EP - 392
AB - 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.
LA - eng
KW - heavy cycles; heavy subgraphs
UR - http://eudml.org/doc/277124
ER -