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On the genus and connectivity of Hamiltonian graphs

✍ Scribed by Richard A. Duke


Publisher
Elsevier Science
Year
1972
Tongue
English
Weight
675 KB
Volume
2
Category
Article
ISSN
0012-365X

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πŸ“œ SIMILAR VOLUMES


On hamiltonian line graphs and connectiv
✍ Siming Zhan πŸ“‚ Article πŸ“… 1991 πŸ› Elsevier Science 🌐 English βš– 444 KB

A well-known conjecture of Thomassen says that every 4-connected line graph is hamiltonian. In this paper we prove that every 7-connected line graph is hamiltonian-connected. For line graph, C. Thomassen [l] made the following conjecture. Conjecture. Every 4-connected line graph is hamiltonian.

On hamiltonian-connected graphs
✍ Ronald J. Gould; Xingxing Yu πŸ“‚ Article πŸ“… 1994 πŸ› John Wiley and Sons 🌐 English βš– 735 KB

## Abstract One of the most fundamental results concerning paths in graphs is due to Ore: In a graph __G__, if deg __x__ + deg __y__ ≧ |__V__(__G__)| + 1 for all pairs of nonadjacent vertices __x, y__ β‰… __V__(__G__), then __G__ is hamiltonian‐connected. We generalize this result using set degrees.

Hamiltonian paths and hamiltonian connec
✍ Bing Wei πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 388 KB

## Let G be a 2-connected graph with n vertices such that d(u)+d(u)+d(w)-IN(u)nN(u)nN(w)I an+ 1 holds for any triple of independent vertices u, v and w. Then for any distinct vertices u and u such that {u, 0) is not a cut vertex set of G, there is a hamiltonian path between u and o. In particular,

On Hamiltonian-connected regular graphs
✍ Ioan Tomescu πŸ“‚ Article πŸ“… 1983 πŸ› John Wiley and Sons 🌐 English βš– 360 KB

In this paper it is shown that any rn-regular graph of order 2rn (rn 3 3), not isomorphic to K, , , , or of order 2rn + 1 (rn even, rn 3 4), is Hamiltonian connected, which extends a previous result of Nash-Williams. As a corollary, it is derived that any such graph contains at least rn Hamiltonian

Hamilton-Connected Cayley Graphs on Hami
✍ Brian Alspach; Yusheng Qin πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 109 KB

It is proven that every connected Cayley graph X , of valency at least three, on a Hamiltonian group is either Hamilton laceable when X is bipartite, or Hamilton connected when X is not bipartite.

All 4-connected Line Graphs of Claw Free
✍ Matthias Kriesell πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 109 KB

Thomassen conjectured that every 4-connected line graph is hamiltonian. Here we shall see that 4-connected line graphs of claw free graphs are hamiltonian connected.