Biembeddings of symmetric configurations and 3-homogeneous Latin trades

Mike J. Grannell; Terry S. Griggs; Martin Knor

Commentationes Mathematicae Universitatis Carolinae (2008)

  • Volume: 49, Issue: 3, page 411-420
  • ISSN: 0010-2628

Abstract

top
Using results of Altshuler and Negami, we present a classification of biembeddings of symmetric configurations of triples in the torus or Klein bottle. We also give an alternative proof of the structure of 3-homogeneous Latin trades.

How to cite

top

Grannell, Mike J., Griggs, Terry S., and Knor, Martin. "Biembeddings of symmetric configurations and 3-homogeneous Latin trades." Commentationes Mathematicae Universitatis Carolinae 49.3 (2008): 411-420. <http://eudml.org/doc/250291>.

@article{Grannell2008,
abstract = {Using results of Altshuler and Negami, we present a classification of biembeddings of symmetric configurations of triples in the torus or Klein bottle. We also give an alternative proof of the structure of 3-homogeneous Latin trades.},
author = {Grannell, Mike J., Griggs, Terry S., Knor, Martin},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {topological embedding; torus; Klein bottle; 6-regular graph; symmetric configuration of triples; partial Latin square; 3-homogeneous Latin trade; topological embedding; torus; Klein bottle; 6-regular graph; symmetric configuration},
language = {eng},
number = {3},
pages = {411-420},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Biembeddings of symmetric configurations and 3-homogeneous Latin trades},
url = {http://eudml.org/doc/250291},
volume = {49},
year = {2008},
}

TY - JOUR
AU - Grannell, Mike J.
AU - Griggs, Terry S.
AU - Knor, Martin
TI - Biembeddings of symmetric configurations and 3-homogeneous Latin trades
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2008
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 49
IS - 3
SP - 411
EP - 420
AB - Using results of Altshuler and Negami, we present a classification of biembeddings of symmetric configurations of triples in the torus or Klein bottle. We also give an alternative proof of the structure of 3-homogeneous Latin trades.
LA - eng
KW - topological embedding; torus; Klein bottle; 6-regular graph; symmetric configuration of triples; partial Latin square; 3-homogeneous Latin trade; topological embedding; torus; Klein bottle; 6-regular graph; symmetric configuration
UR - http://eudml.org/doc/250291
ER -

References

top
  1. Altshuler A., 10.1016/S0012-365X(73)80002-0, Discrete Math. 115 (1973), 201-217. (1973) Zbl0253.05117MR0321797DOI10.1016/S0012-365X(73)80002-0
  2. Cavenagh N.J., A uniqueness result for 3 -homogeneous Latin trades, Comment. Math. Univ. Carolin. 47 (2006), 337-358. (2006) Zbl1138.05007MR2241536
  3. Cavenagh N.J., Donovan D.M., Drápal A., 10.1016/j.disc.2005.04.021, Discrete Math. 300 (2005), 57-70. (2005) Zbl1073.05012MR2170114DOI10.1016/j.disc.2005.04.021
  4. Colbourn C.J., Rosa A., Triple Systems, Clarendon Press, New York, 1999, ISBN: 0-19-853576-7. Zbl1030.05017MR1843379
  5. Donovan D.M., Drápal A., Lefevre J.G., Permutation representation of 3 and 4 -homogeneous Latin bitrades, submitted. 
  6. Figueroa-Centeno R.M., White A.T., 10.1016/S0378-3758(99)00122-6, J. Statist. Plann. Inference 86 (2000), 421-434. (2000) Zbl0973.05014MR1768283DOI10.1016/S0378-3758(99)00122-6
  7. Grannell M.J., Griggs T.S., Designs and topology, in Surveys in Combinatorics 2007, London Math. Soc. Lecture Note Series 346, Cambridge University Press, Cambridge, 2007, pp.121-174. MR2252792
  8. Grannell M.J., Griggs T.S., Knor M., 10.1017/S0017089504001922, Glasgow Math. J. 46 (2004), 443-457. (2004) Zbl1062.05030MR2094802DOI10.1017/S0017089504001922
  9. Grannell M.J., Griggs T.S., Knor M., Biembeddings of symmetric configurations of triples, Proceedings of MaGiA conference, Kočovce 2004, Slovak University of Technology, 2004, pp.106-112. 
  10. Hämäläinen C., Partitioning 3 -homogeneous latin bitrades, preprint. MR2390076
  11. Kirkman T.P., On a problem of combinations, Cambridge and Dublin Math. J. 2 (1847), 191-204. (1847) 
  12. Lawrencenko S., Negami S., 10.1006/jctb.1999.1920, J. Combin. Theory Ser. B 77 (1999), 211-218. (1999) Zbl1025.05018MR1710539DOI10.1006/jctb.1999.1920
  13. Lefevre J.G., Donovan D.M., Grannell M.J., Griggs T.S., A constraint on the biembedding of Latin squares, submitted. Zbl1170.05017
  14. Negami S., 10.1016/0012-365X(83)90057-2, Discrete Math. 44 (1983), 161-180. (1983) Zbl0508.05033MR0689809DOI10.1016/0012-365X(83)90057-2
  15. Negami S., Classification of 6 -regular Klein-bottlal graphs, Research Reports on Information Sciences, Department of Information Sciences, Tokyo Institute of Technology A-96 (1984), 16pp. (1984) 
  16. White A.T., 10.1016/S0012-365X(01)00069-3, Discrete Math. 244 (2002), 479-493. (2002) Zbl0989.05025MR1844056DOI10.1016/S0012-365X(01)00069-3

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.