### Abstract

We prove the following theorem: For a connected noncomplete graph G, let τ(G): = min{d_{G}(u) + d_{G}(v)|d_{G}(u, v) = 2}. Suppose G is a 3-connected noncomplete graph. Then through each edge of G there passes a cycle of length ≥ min{|V(G)|, τ(G) - 1}.

Original language | English |
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Pages (from-to) | 275-279 |

Number of pages | 5 |

Journal | Journal of Graph Theory |

Volume | 24 |

Issue number | 3 |

Publication status | Published - 1997 Mar |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Journal of Graph Theory*,

*24*(3), 275-279.

**Long Cycles Passing Through a Specified Edge in a 3-Connected Graph.** / Enomoto, Hikoe; Hirohata, Kazuhide; Ota, Katsuhiro.

Research output: Contribution to journal › Article

*Journal of Graph Theory*, vol. 24, no. 3, pp. 275-279.

}

TY - JOUR

T1 - Long Cycles Passing Through a Specified Edge in a 3-Connected Graph

AU - Enomoto, Hikoe

AU - Hirohata, Kazuhide

AU - Ota, Katsuhiro

PY - 1997/3

Y1 - 1997/3

N2 - We prove the following theorem: For a connected noncomplete graph G, let τ(G): = min{dG(u) + dG(v)|dG(u, v) = 2}. Suppose G is a 3-connected noncomplete graph. Then through each edge of G there passes a cycle of length ≥ min{|V(G)|, τ(G) - 1}.

AB - We prove the following theorem: For a connected noncomplete graph G, let τ(G): = min{dG(u) + dG(v)|dG(u, v) = 2}. Suppose G is a 3-connected noncomplete graph. Then through each edge of G there passes a cycle of length ≥ min{|V(G)|, τ(G) - 1}.

UR - http://www.scopus.com/inward/record.url?scp=0347076283&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0347076283&partnerID=8YFLogxK

M3 - Article

VL - 24

SP - 275

EP - 279

JO - Journal of Graph Theory

JF - Journal of Graph Theory

SN - 0364-9024

IS - 3

ER -