Circumferences of 3-connected claw-free graphs

Zhi-Hong Chen

doi:10.1016/j.disc.2016.01.018

Circumferences of 3-connected claw-free graphs

Zhi-Hong Chen

Butler University

Research output: Contribution to journal › Article › peer-review

Abstract

In Li et al. (2009), proved that a 3-connected claw-free graph of order n with minimum degree δ contains a cycle of length at least min{ n ,6δ−15} , and they conjectured that such graphs should have a cycle of length at least min{ n ,9δ−3} . We prove that this conjecture is true with δ≥8 .

Original language	American English
Journal	Discrete Mathematics
Volume	339
Issue number	6
DOIs	https://doi.org/10.1016/j.disc.2016.01.018
State	Published - Jun 2016

Keywords

Circumference
Claw-free graph
Closed trail
Collapsible graph
Dominating closed trail
Supereulerian graph

Disciplines

Computer Sciences
Mathematics

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10.1016/j.disc.2016.01.018License: Unspecified

Cite this

@article{8a92d45423fc4793af989ed6108434db,

title = "Circumferences of 3-connected claw-free graphs",

abstract = " In Li et al. (2009), proved that a 3-connected claw-free graph of order n with minimum degree δ contains a cycle of length at least min\{ n ,6δ−15\} , and they conjectured that such graphs should have a cycle of length at least min\{ n ,9δ−3\} . We prove that this conjecture is true with δ≥8 . ",

keywords = "Circumference, Claw-free graph, Closed trail, Collapsible graph, Dominating closed trail, Supereulerian graph",

author = "Zhi-Hong Chen",

note = "Get this from a library! Circumferences of 3-connected claw-free graphs. [Chen Z.-H.]",

year = "2016",

month = jun,

doi = "10.1016/j.disc.2016.01.018",

language = "American English",

volume = "339",

journal = "Discrete Mathematics",

issn = "0012-365X",

number = "6",

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TY - JOUR

T1 - Circumferences of 3-connected claw-free graphs

AU - Chen, Zhi-Hong

N1 - Get this from a library! Circumferences of 3-connected claw-free graphs. [Chen Z.-H.]

PY - 2016/6

Y1 - 2016/6

N2 - In Li et al. (2009), proved that a 3-connected claw-free graph of order n with minimum degree δ contains a cycle of length at least min{ n ,6δ−15} , and they conjectured that such graphs should have a cycle of length at least min{ n ,9δ−3} . We prove that this conjecture is true with δ≥8 .

AB - In Li et al. (2009), proved that a 3-connected claw-free graph of order n with minimum degree δ contains a cycle of length at least min{ n ,6δ−15} , and they conjectured that such graphs should have a cycle of length at least min{ n ,9δ−3} . We prove that this conjecture is true with δ≥8 .

KW - Circumference

KW - Claw-free graph

KW - Closed trail

KW - Collapsible graph

KW - Dominating closed trail

KW - Supereulerian graph

UR - http://www.worldcat.org/oclc/6004491246

U2 - 10.1016/j.disc.2016.01.018

DO - 10.1016/j.disc.2016.01.018

M3 - Article

SN - 0012-365X

VL - 339

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 6

ER -

Circumferences of 3-connected claw-free graphs

Abstract

Keywords

Disciplines

Access to Document

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