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

Hikoe Enomoto; Kazuhide Hirohata; Katsuhiro Ota

doi:10.1002/(SICI)1097-0118(199703)24:3<275::AID-JGT9>3.0.CO;2-M

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

Hikoe Enomoto
, Kazuhide Hirohata
, Katsuhiro Ota

Department of Mathematics

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

2 Citations (Scopus)

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
Pages (from-to)	275-279
Number of pages	5
Journal	Journal of Graph Theory
Volume	24
Issue number	3
DOIs	https://doi.org/10.1002/(SICI)1097-0118(199703)24:3<275::AID-JGT9>3.0.CO;2-M
Publication status	Published - 1997 Mar

ASJC Scopus subject areas

Geometry and Topology

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10.1002/(SICI)1097-0118(199703)24:3<275::AID-JGT9>3.0.CO;2-M

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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\}.",

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AU - Ota, Katsuhiro

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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}.

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

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