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

Hikoe Enomoto, Kazuhide Hirohata, Katsuhiro Ota

Research output: Contribution to journalArticle

2 Citations (Scopus)

### Abstract

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}.

Original language English 275-279 5 Journal of Graph Theory 24 3 Published - 1997 Mar

Long Cycle
Connected graph
Cycle
Theorem

### ASJC Scopus subject areas

• Mathematics(all)

### Cite this

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

In: Journal of Graph Theory, Vol. 24, No. 3, 03.1997, p. 275-279.

Research output: Contribution to journalArticle

Enomoto, Hikoe ; Hirohata, Kazuhide ; Ota, Katsuhiro. / Long Cycles Passing Through a Specified Edge in a 3-Connected Graph. In: Journal of Graph Theory. 1997 ; Vol. 24, No. 3. pp. 275-279.
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