We prove that any connected graph that contains no subdivision of an β΅ 1regular tree has an end-faithful spanning tree; and furthermore that it has a rayless spanning tree if all its ends are dominated. This improves a result of Seymour and Thomas (An end-faithful spanning tree counterexample, Discr
An end-faithful spanning tree counterexample
β Scribed by Paul Seymour; Robin Thomas
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 980 KB
- Volume
- 95
- Category
- Article
- ISSN
- 0012-365X
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π SIMILAR VOLUMES
We refer to for terminology not specified here. Graphs mentioned in this note are undirected, simple. The following definition is due to Halin [l]: an end E of an infinite graph G is a set of l-way infinite paths in G such that P, Q E E iff for any finite subset R of V(G) there is a finite path in
## 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
If a graph G with cycle rank p contains both spanning trees with rn and with n end-vertices, rn < n, then G has at least 2p spanning trees with k end-vertices for each integer k, rn < k < n. Moreover, the lower bound of 2p is best possible. [ l ] and Schuster [4] independently proved that such span