𝔖 Bobbio Scriptorium
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Spanning trees with many leaves

✍ Scribed by D. V. Karpov


Publisher
Springer US
Year
2011
Tongue
English
Weight
211 KB
Volume
179
Category
Article
ISSN
1573-8795

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Spanning trees with many leaves
✍ Guoli Ding; Thor Johnson; Paul Seymour πŸ“‚ Article πŸ“… 2001 πŸ› John Wiley and Sons 🌐 English βš– 95 KB

## Abstract We show that if __G__ is a simple connected graph with and $|V(G)| \,\neq\,t+2$, then __G__ has a spanning tree with > __t__ leaves, and this is best possible. Β© 2001 John Wiley & Sons, Inc. J Graph Theory 37: 189–197, 2001

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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.