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.
β¦ LIBER β¦
Spanning Trees with Few Leaves
β Scribed by Masao Tsugaki; Tomoki Yamashita
- Publisher
- Springer Japan
- Year
- 2007
- Tongue
- English
- Weight
- 272 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0911-0119
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## Abstract We show that if __G__ is a simple connected graph with and $|V(G)| \,\neq\,t+2$, then __G__ has a spanning tree withβ>β__t__ leaves, and this is best possible. Β© 2001 John Wiley & Sons, Inc. J Graph Theory 37: 189β197, 2001
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