# Heavy Subgraph Conditions for Longest Cycles to Be Heavy in Graphs

Discussiones Mathematicae Graph Theory (2016)

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

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topBinlong 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

top- [1] B. Bollobás and G. Brightwell, Cycles through specified vertices, Combinatorica 13 (1993) 147-155. doi:10.1007/BF01303200[Crossref] Zbl0780.05033
- [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] 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] 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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