Heavy Subgraph Conditions for Longest Cycles to Be Heavy in Graphs

Binlong Lia; Shenggui Zhang

Discussiones Mathematicae Graph Theory (2016)

  • Volume: 36, Issue: 2, page 383-392
  • ISSN: 2083-5892

Abstract

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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.

How to cite

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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 -

References

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  1. [1] B. Bollobás and G. Brightwell, Cycles through specified vertices, Combinatorica 13 (1993) 147-155. doi:10.1007/BF01303200[Crossref] Zbl0780.05033
  2. [2] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (Macmillan, Lon- don and Elsevier, New York, 1976). doi:10.1007/978-1-349-03521-2[Crossref] 
  3. [3] G. Fan, New sufficient conditions for cycles in graphs, J. Combin. Theory Ser. B 37 (1984) 221-227. doi:10.1016/0095-8956(84)90054-6[Crossref] 
  4. [4] R. Shi, 2-neighborhoods and hamiltonian conditions, J. Graph Theory 16 (1992) 267-271. doi:10.1002/jgt.3190160310[Crossref] Zbl0761.05066

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