KMS Of Academy of mathematics and systems sciences, CAS
Fan-type theorem for path-connectivity | |
Hu, ZQ; Tian, F; Wei, B; Egawa, Y; Hirohata, K | |
2002-04-01 | |
Source Publication | JOURNAL OF GRAPH THEORY |
ISSN | 0364-9024 |
Volume | 39Issue:4Pages:265-282 |
Abstract | For 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. |
Keyword | cycle path subvine |
DOI | 10.1002/jgt.10028 |
Language | 英语 |
WOS Research Area | Mathematics |
WOS Subject | Mathematics |
WOS ID | WOS:000174516000005 |
Publisher | JOHN WILEY & SONS INC |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/17849 |
Collection | 中国科学院数学与系统科学研究院 |
Corresponding Author | Hu, ZQ |
Affiliation | 1.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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