On the spanning trees of weighted graphs
β Scribed by Ernst W. Mayr; C. Greg Plaxton
- Publisher
- Springer-Verlag
- Year
- 1992
- Tongue
- English
- Weight
- 874 KB
- Volume
- 12
- Category
- Article
- ISSN
- 0209-9683
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let G be a 2-connected weighted graph and k β₯ 2 an integer. In this note we prove that if the sum of the weighted degrees of every k + 1 pairwise nonadjacent vertices is at least m, then G contains either a cycle of weight at least 2m/(k + 1) or a spanning tree with no more than k leaves.
Let 3:; denote the set of simple graphs with n vertices and m edges, t ( G ) the number of spanning trees of a graph G , and F 2 H if t(K,\E(F))?t(K,\E(H)) for every s? max{u(F), u ( H ) } . We give a complete characterization of >-maximal (maximum) graphs in 3:; subject to m 5 n . This result conta