Counting k-component forests of a graph
β Scribed by Wendy Myrvold
- Publisher
- John Wiley and Sons
- Year
- 1992
- Tongue
- English
- Weight
- 331 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0028-3045
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Favaron, MahΓ©o, and SaclΓ© proved that the residue of a simple graph G is a lower bound on its independence number Ξ±(G). For k β N, a vertex set X in a graph is called k-independent, if the subgraph induced by X has maximum degree less than k. We prove that a generalization of the residue, the k-resi
We prove that, in a random graph with n vertices and N = cn log n edges, the subgraph generated by a set of all vertices of degree at least k + 1 is k-leaf connected for c > f . A threshold function for k-leaf connectivity is also found. ## 1. MAIN RESULTS Let G = (V(G),E(G)) be a graph, where V (
We observe that the values of p for which with high probability Gm,p is k-colorable and for which with high probability G,,p has no k-core are not equal for k 2 4.
## Abstract We show via an exhaustive computer search that there does not exist a (__K__~6~β__e__)βdecomposition of __K__~29~. This is the first example of a nonβcomplete graph __G__ for which a __G__βdecomposition of __K__~2|E(G)|+__1__~ does not exist. Β© 2009 Wiley Periodicals, Inc. J Combin Desi