Fan-type theorem for path-connectivity
Hu, ZQ; Tian, F; Wei, B; Egawa, Y; Hirohata, K
AbstractFor a connected noncomplete graph G, let mu(G) = min{max {d(G)(u), d(G)(v)}:d(G)(u, v)=2}. A well-known theorem of Fan says that every 2-connected noncomplete graph has a cycle of length at least min{\V(G)\, 2mu(G)}. In this paper, we prove the following Fan-type theorem: if G is a 3-connected noncomplete graph, then each pair of distinct vertices of G is joined by a path of length at least min{\V(G)\-1, 2mu(G) - 2}. As consequences, we have: (i) if G is a 3-connected noncomplete graph with mu(G) > \V(G)\/2, then G is Hamilton-connected; (ii) if G is a (s + 2)-connected noncomplete graph, where s greater than or equal to 1 is an integer, then through each path of length s of G there passes a cycle of length greater than or equal to min{\V(G)\, 2mu(G) - s}. Several results known before are generalized and a conjecture of Enomoto, Hirohata, and Ota is proved. (C) 2002 Wiley Periodicals, Inc.
Keywordcycle path subvine
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000174516000005
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Document Type期刊论文
Corresponding AuthorHu, ZQ
Affiliation1.Cent China Normal Univ, Dept Math, Lab Nonlinear Anal, Wuhan 430079, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Beijing 100080, Peoples R China
3.Sci Univ Tokyo, Dept Math Appl, Shinjuku Ku, Tokyo 1628601, Japan
4.Ibaraki Natl Coll Technol, Dept Elect & Comp Engn, Ibaraki 3128508, Japan
Recommended Citation
GB/T 7714
Hu, ZQ,Tian, F,Wei, B,et al. Fan-type theorem for path-connectivity[J]. JOURNAL OF GRAPH THEORY,2002,39(4):265-282.
APA Hu, ZQ,Tian, F,Wei, B,Egawa, Y,&Hirohata, K.(2002).Fan-type theorem for path-connectivity.JOURNAL OF GRAPH THEORY,39(4),265-282.
MLA Hu, ZQ,et al."Fan-type theorem for path-connectivity".JOURNAL OF GRAPH THEORY 39.4(2002):265-282.
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