Collapsible graphs and Hamiltonian connectedness of line graphs
- 数学科学－已发表论文 
Thomassen conjectured that every 4-connected line graph is Hamiltonian. Chen and Lai [Z.-H. Chen, H.-J. Lai, Reduction techniques for super-Eulerian graphs and related topics an update, in: Ku Tung-Hsin (Ed.), Combinatorics and Graph Theory, vol. 95, World Scientific, Singapore/London, 1995, pp. 53-69, Conjecture 8.6] conjectured that every 3-edge connected, essentially 6-edge connected graph is collapsible. In this paper, we prove the following results. (1) Every 3-edge connected, essentially 6-edge connected graph with edge-degree at least 7 is collapsible. (2) Every 3-edge connected, essentially 5-edge connected graph with edge-degree at least 6 and at most 24 vertices of degree 3 is collapsible which implies that 5-connected line graph with minimum degree at least 6 of a graph with at most 24 vertices of degree 3 is Hamiltonian. (3) Every 3-connected, essentially 11-connected line graph is Hamilton-connected which strengthens the result in [H.-J. Lai, Y. Shao, H. Wu, J. Zhou, Every 3-connected, essentially 11-connected line graph is Hamiltonian, J. Combin. Theory, Ser. B 96 (2006) 571-576] by Lai et al. (4) Every 7-connected line graph is Hamiltonian connected which is proved by a method different from Zhan's. By using the multigraph closure introduced by Ryjacek and Vrana which turns a claw-free graph into the line graph of a multigraph while preserving its Hamilton-connectedness, the results (3) and (4) can be extended to claw-free graphs. (C) 2012 Elsevier B.V. All rights reserved.
CitationDISCRETE APPLIED MATHEMATICS，2012,160（12）：1837-1844
Showing items related by title, author, creator and subject.
Yang, Weihua; Xiong, Liming; Lai, Hongjian; Guo, Xiaofeng; 郭晓峰 (PERGAMON-ELSEVIER SCIENCE LTD, 2012-10)Thomassen conjectured that every 4-connected line graph is Hamiltonian. Lai et al. conjectured [H. Lai, Y. Shao, H. Wu, J. Zhou, Every 3-connected, essentially 11-connected line graph is Hamiltonian, J. Combin. Theory Ser. ...
林泓; 郭晓峰 (2009)令g是一个简单连通图.设S■V(g)且|S|=2n+1,将S收缩为一个顶点后所得到的图记α_((2n+1))(g,S).若g有完美匹配,且对于V(g)的任意一个有2n+1个顶点的子集S,图α_((2n+1))(g,S)有完美匹配,则称g是一个(2n+1)-可收缩图.设S_1,S_2,…,S_(2n)是V(g)的两两不相交的子集且|S_1|=|S_2|=…=|S_(2n)|=2,将S_I (I=1,2,…,2n)分别收缩为一点所得到的图记 ...
奇图的匹配可扩性 翟绍辉; 郭晓峰 (2009)设g是一个图,n,k和d是三个非负整数,满足n+2k+d≤|V(g)|-2,|V(g)|和n+d有相同的奇偶性.如果删去g中任意n个点后所得的图有k-匹配,并且任一k-匹配都可以扩充为一个亏d-匹配,那么称g是一个(n,k,d)-图.lIu和yu首先引入了(n,k,d)-图的概念,并且给出了(n,k,d)-图的一个刻划和若干性质.(0,k,1)-图也称为几乎k-可扩图.在本文中,作者改进了(n,k,d)-图的刻划,并给出了几乎k-可扩图 ...