We prove that, with very few exceptions, every graph of order n, n = 0, 1 (mod 4) and size a t most n -1, is contained in a self-complementary graph of order n. We study a similar problem for digraphs. Throughout the paper, G and D will denote a finite graph and a finite digraph, respectively, with
Balancing two spanning trees
β Scribed by Matthias Kriesell
- Publisher
- John Wiley and Sons
- Year
- 2010
- Tongue
- English
- Weight
- 80 KB
- Volume
- 57
- Category
- Article
- ISSN
- 0028-3045
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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
We present an algorithm for counting the number of minimum weight spanning trees, based on the fact that the generating function for the number of spanning trees of a given graph, by weight, can be expressed as a simple determinant. For a graph with n vertices and m edges, our Ε½ Ε½ .. Ε½ . algorithm r
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