| Title:
|
End-faithful spanning trees of countable graphs with prescribed sets of rays (English) |
| Author:
|
Polat, Norbert |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
51 |
| Issue:
|
1 |
| Year:
|
2001 |
| Pages:
|
45-53 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that a countable connected graph has an end-faithful spanning tree that contains a prescribed set of rays whenever this set is countable, and we show that this solution is, in a certain sense, the best possible. This improves a result of Hahn and Širáň Theorem 1. (English) |
| MSC:
|
05C05 |
| MSC:
|
05C25 |
| MSC:
|
05C38 |
| MSC:
|
05C99 |
| idZBL:
|
Zbl 1079.05508 |
| idMR:
|
MR1814631 |
| . |
| Date available:
|
2009-09-24T10:39:39Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127625 |
| . |
| Reference:
|
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| Reference:
|
[2] G. Hahn and J. Širáň: Three remarks on end-faithfulness.Finite and Infinite Combinatorics in Sets and Logic, N. Sauer et al. (eds.), Kluwer, 1993, pp. 125–133. MR 1261200 |
| Reference:
|
[3] R. Halin: Über unendliche Wege in Graphen.Math. Ann. 157 (1964), 125–137. Zbl 0125.11701, MR 0170340, 10.1007/BF01362670 |
| Reference:
|
[4] H. Hopf: Enden offener Raüme und unendliche diskontinuierliche Gruppen.Comm. Math. Helv. 15 (1943), 27–32. MR 0007646 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[8] P. Seymour and R. Thomas: An end-faithful spanning tree counterexample.Discrete Math. 95 (1991), 321–330. MR 1045600, 10.1016/0012-365X(91)90344-2 |
| Reference:
|
[9] J. Širáň: End-faithful forests and spanning trees in infinite graphs.Discrete Math. 95 (1991), 331–340. MR 1141946, 10.1016/0012-365X(91)90345-3 |
| Reference:
|
[10] C. Thomassen: Infinite connected graphs with no end-preserving spanning trees.J. Combin. Theory Ser. B 54 (1992), 322–324. Zbl 0753.05030, MR 1152455, 10.1016/0095-8956(92)90059-7 |
| . |
