Let k be an odd integer /> 3, and G be a connected graph of odd order n with n/>4k -3, and minimum degree at least k. In this paper it is proved that if for each pair of nonadjacent vertices u, v in G max{dG(u), d~(v)} >~n/2, then G has an almost k--factor F + and a matching M such that F-and M are
On the 1-factors of n-connected graphs
β Scribed by Joseph Zaks
- Publisher
- Elsevier Science
- Year
- 1971
- Tongue
- English
- Weight
- 664 KB
- Volume
- 11
- Category
- Article
- ISSN
- 0095-8956
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π SIMILAR VOLUMES
The main aim of the present note is the proof of a variant of the MENGER-WHITNEY theorem on n-connected graphs (Theorem 1 below). While the result itself is well known (being, for example, a special case of the theorem of MENGER mentioned in Remark I), two of its aspects deserve attention. First, it
## Abstract We consider the existence of several different kinds of factors in 4βconnected clawβfree graphs. This is motivated by the following two conjectures which are in fact equivalent by a recent result of the third author. Conjecture 1 (Thomassen): Every 4βconnected line graph is hamiltonian,
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