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
The number of 1-factors in 2k-connected graphs
✍ Scribed by Béla Bollobas
- Publisher
- Elsevier Science
- Year
- 1978
- Tongue
- English
- Weight
- 166 KB
- Volume
- 25
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
Let G be a graph with vertex set V (G). In this work we present a sufficient condition for the existence of connected [k, k + 1]factors in graphs. The condition involves the stability number and degree conditions of graph G.
In this article, we study the existence of a 2-factor in a K 1,nfree graph. Sumner [J London Math Soc 13 (1976), 351-359] proved that for n ≥ 4, an (n-1)-connected K 1,n -free graph of even order has a 1-factor.
## Abstract An (__n, q__) graph has __n__ labeled points, __q__ edges, and no loops or multiple edges. The number of connected (__n, q__) graphs is __f(n, q)__. Cayley proved that __f(n, n__^‐1^) = __n__^n−2^ and Renyi found a formula for __f(n, n)__. Here I develop two methods to calculate the exp