## Abstract The following interpolation theorem is proved: If a graph __G__ contains spanning trees having exactly __m__ and __n__ endβvertices, with __m__ < __n__, then for every integer __k, m < k < n, G__ contains a spanning tree having exactly __k__ endβvertices. This settles a problem posed by
The independence number condition for the existence of a spanning f-tree
β Scribed by Hikoe Enomoto; Kenta Ozeki
- Publisher
- John Wiley and Sons
- Year
- 2010
- Tongue
- English
- Weight
- 123 KB
- Volume
- 65
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
Let G be a graph and f be a mapping from V(G) to the positive integers. A subgraph T of G is called an fβtree if T forms a tree and d~T~(x)β€f(x) for any xβV(T). We propose a conjecture on the existence of a spanning fβtree, and give a partial solution to it. Β© 2009 Wiley Periodicals, Inc. J Graph Theory 65:
173β184, 2010
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