## Abstract We consider finite undirected loopless graphs __G__ in which multiple edges are possible. For integers k,l β₯ 0 let g(k, l) be the minimal __n__ β₯ 0 with the following property: If __G__ is an __n__βedgeβconnected graph, __s__~1~, β,__s__~k~, __t__~1~, β,__t__~k~ are vertices of __G__, a
Paths and edge-connectivity in graphs
β Scribed by Haruko Okamura
- Publisher
- Elsevier Science
- Year
- 1984
- Tongue
- English
- Weight
- 903 KB
- Volume
- 37
- Category
- Article
- ISSN
- 0095-8956
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## 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,
## Abstract A result of G. Chartrand, A. Kaugars, and D. R. Lick [Proc Amer Math Soc 32 (1972), 63β68] says that every finite, kβconnected graph __G__ of minimum degree at least β3__k__/2β contains a vertex __x__ such that __G__β__x__ is still __k__βconnected. We generalize this result by proving t