Non-uniform random spanning trees on weighted graphs
β Scribed by M. Mosbah; N. Saheb
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 547 KB
- Volume
- 218
- Category
- Article
- ISSN
- 0304-3975
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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.
## Abstract Motivated by the observation that the sparse treeβlike subgraphs in a small world graph have large diameter, we analyze random spanning trees in a given host graph. We show that the diameter of a random spanning tree of a given host graph __G__ is between and with high probability., w