End-faithful spanning trees of countable graphs with prescribed sets of rays

Norbert Polat

Czechoslovak Mathematical Journal (2001)

  • Volume: 51, Issue: 1, page 45-53
  • ISSN: 0011-4642

Abstract

top
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.

How to cite

top

Polat, Norbert. "End-faithful spanning trees of countable graphs with prescribed sets of rays." Czechoslovak Mathematical Journal 51.1 (2001): 45-53. <http://eudml.org/doc/30613>.

@article{Polat2001,
abstract = {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.},
author = {Polat, Norbert},
journal = {Czechoslovak Mathematical Journal},
keywords = {countable graph; end-faithful graph; spanning trees},
language = {eng},
number = {1},
pages = {45-53},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {End-faithful spanning trees of countable graphs with prescribed sets of rays},
url = {http://eudml.org/doc/30613},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Polat, Norbert
TI - End-faithful spanning trees of countable graphs with prescribed sets of rays
JO - Czechoslovak Mathematical Journal
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 1
SP - 45
EP - 53
AB - 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.
LA - eng
KW - countable graph; end-faithful graph; spanning trees
UR - http://eudml.org/doc/30613
ER -

References

top
  1. 10.1007/BF02566233, Comment. Math. Helv. 17 (1944), 1–38. (1944) MR0012214DOI10.1007/BF02566233
  2. Three remarks on end-faithfulness, Finite and Infinite Combinatorics in Sets and Logic, N. Sauer et al. (eds.), Kluwer, 1993, pp. 125–133. (1993) MR1261200
  3. 10.1007/BF01362670, Math. Ann. 157 (1964), 125–137. (1964) Zbl0125.11701MR0170340DOI10.1007/BF01362670
  4. Enden offener Raüme und unendliche diskontinuierliche Gruppen, Comm. Math. Helv. 15 (1943), 27–32. (1943) MR0007646
  5. 10.1002/mana.19821070124, Math. Nachr. 107 (1982), 283–314. (1982) Zbl0536.05043MR0695755DOI10.1002/mana.19821070124
  6. 10.1006/jctb.1996.0035, J. Combin. Theory Ser. B 67 (1996), 86–110. (1996) Zbl0855.05051MR1385385DOI10.1006/jctb.1996.0035
  7. 10.1006/jctb.1996.0057, J. Combin. Theory Ser. B 68 (1996), 56–86. (1996) Zbl0855.05052MR1405706DOI10.1006/jctb.1996.0057
  8. 10.1016/0012-365X(91)90344-2, Discrete Math. 95 (1991), 321–330. (1991) MR1045600DOI10.1016/0012-365X(91)90344-2
  9. 10.1016/0012-365X(91)90345-3, Discrete Math. 95 (1991), 331–340. (1991) MR1141946DOI10.1016/0012-365X(91)90345-3
  10. 10.1016/0095-8956(92)90059-7, J. Combin. Theory Ser. B 54 (1992), 322–324. (1992) Zbl0753.05030MR1152455DOI10.1016/0095-8956(92)90059-7

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.