## 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
Graphs with not too many spanning trees
β Scribed by Guoli Ding
- Publisher
- John Wiley and Sons
- Year
- 1995
- Tongue
- English
- Weight
- 458 KB
- Volume
- 25
- Category
- Article
- ISSN
- 0028-3045
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π SIMILAR VOLUMES
The distance between a pair of vertices u, u in a graph G is the length of a shortest path joining u and u. The diameter diam(G) of G is the maximum distance between all pairs of vertices in G. A spanning tree Tof G is diameter preserving if diam(T) = diam(G). In this note, we characterize graphs th
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