Fan-Type Theorem for Long Cycles Containing a Specified Edge |
| |
| Authors: | Mei Lu Huiqing Liu Feng Tian |
| |
| Institution: | (1) Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China;(2) School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, China;(3) Institute of Systems Science, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, 100080, China |
| |
| Abstract: | In this paper, we prove that if G is 3-connected noncomplete graph of order n satisfying min{max{d(u),d(v)}:d(u,v)=2}=μ, then for each edge e, G has a cycle containing e of length at least min{n,2μ}, unless G is a spanning subgraph of Kμ + Kcn−μ or K3+(lKμ−2∪Ks), where n=l(μ−2)+s+3,1≤s≤μ−2.
Partially supported by NNSFC(No. 60172005);
Partially supported by NNSFC(No. 10431020); |
| |
| Keywords: | Cycle Specified edge Complete subgraph |
| 本文献已被 SpringerLink 等数据库收录！ |
|
