Heavy Subgraph Conditions for Longest Cycles to Be Heavy in Graphs

Heavy Subgraph Conditions for Longest Cycles to Be Heavy in Graphs

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 e...

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Bibliographic Details
Main Authors: Lia Binlong, Zhang Shenggui
Format: Article
Language:English
Published: Sciendo 2016-05-01
Series:Discussiones Mathematicae Graph Theory
Subjects:
heavy cycles
heavy subgraphs
Online Access:https://doi.org/10.7151/dmgt.1863
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spelling doaj-2c00d234d7704d0baa12449c43f86f2d2021-09-05T17:20:21ZengSciendoDiscussiones Mathematicae Graph Theory2083-58922016-05-0136238339210.7151/dmgt.1863dmgt.1863Heavy Subgraph Conditions for Longest Cycles to Be Heavy in GraphsLia Binlong0Zhang Shenggui1Department of Applied Mathematics, Northwestern Polytechnical UniversityXi′an, Shaanxi 710072, P.R.ChinaDepartment of Applied Mathematics, Northwestern Polytechnical UniversityXi′an, Shaanxi 710072, P.R.ChinaLet 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.https://doi.org/10.7151/dmgt.1863heavy cyclesheavy subgraphs
collection DOAJ
language English
format Article
sources DOAJ
author Lia Binlong
Zhang Shenggui
spellingShingle Lia Binlong
Zhang Shenggui
Heavy Subgraph Conditions for Longest Cycles to Be Heavy in Graphs
Discussiones Mathematicae Graph Theory
heavy cycles
heavy subgraphs
author_facet Lia Binlong
Zhang Shenggui
author_sort Lia Binlong
title Heavy Subgraph Conditions for Longest Cycles to Be Heavy in Graphs
title_short Heavy Subgraph Conditions for Longest Cycles to Be Heavy in Graphs
title_full Heavy Subgraph Conditions for Longest Cycles to Be Heavy in Graphs
title_fullStr Heavy Subgraph Conditions for Longest Cycles to Be Heavy in Graphs
title_full_unstemmed Heavy Subgraph Conditions for Longest Cycles to Be Heavy in Graphs
title_sort heavy subgraph conditions for longest cycles to be heavy in graphs
publisher Sciendo
series Discussiones Mathematicae Graph Theory
issn 2083-5892
publishDate 2016-05-01
description 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.
topic heavy cycles
heavy subgraphs
url https://doi.org/10.7151/dmgt.1863
work_keys_str_mv AT liabinlong heavysubgraphconditionsforlongestcyclestobeheavyingraphs
AT zhangshenggui heavysubgraphconditionsforlongestcyclestobeheavyingraphs
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