| Title:
|
Biembeddings of symmetric configurations and 3-homogeneous Latin trades (English) |
| Author:
|
Grannell, M. J. |
| Author:
|
Griggs, T. S. |
| Author:
|
Knor, M. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
49 |
| Issue:
|
3 |
| Year:
|
2008 |
| Pages:
|
411-420 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
topological embedding |
| Keyword:
|
torus |
| Keyword:
|
Klein bottle |
| Keyword:
|
6-regular graph |
| Keyword:
|
symmetric configuration of triples |
| Keyword:
|
partial Latin square |
| Keyword:
|
3-homogeneous Latin trade |
| MSC:
|
05B15 |
| MSC:
|
05B30 |
| MSC:
|
05C10 |
| idZBL:
|
Zbl 1212.05053 |
| idMR:
|
MR2490436 |
| . |
| Date available:
|
2009-05-05T17:12:04Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119732 |
| . |
| Reference:
|
[1] Altshuler A.: Construction and enumeration of regular maps on the torus.Discrete Math. 115 (1973), 201-217. Zbl 0253.05117, MR 0321797, 10.1016/S0012-365X(73)80002-0 |
| Reference:
|
[2] Cavenagh N.J.: A uniqueness result for $3$-homogeneous Latin trades.Comment. Math. Univ. Carolin. 47 (2006), 337-358. Zbl 1138.05007, MR 2241536 |
| Reference:
|
[3] Cavenagh N.J., Donovan D.M., Drápal A.: $3$-homogeneous Latin trades.Discrete Math. 300 (2005), 57-70. Zbl 1073.05012, MR 2170114, 10.1016/j.disc.2005.04.021 |
| Reference:
|
[4] Colbourn C.J., Rosa A.: Triple Systems.Clarendon Press, New York, 1999, ISBN: 0-19-853576-7. Zbl 1030.05017, MR 1843379 |
| Reference:
|
[5] Donovan D.M., Drápal A., Lefevre J.G.: Permutation representation of $3$ and $4$-homogeneous Latin bitrades.submitted. |
| Reference:
|
[6] Figueroa-Centeno R.M., White A.T.: Topological models for classical configurations.J. Statist. Plann. Inference 86 (2000), 421-434. Zbl 0973.05014, MR 1768283, 10.1016/S0378-3758(99)00122-6 |
| Reference:
|
[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. MR 2252792 |
| Reference:
|
[8] Grannell M.J., Griggs T.S., Knor M.: Biembeddings of Latin squares and Hamiltonian decompositions.Glasgow Math. J. 46 (2004), 443-457. Zbl 1062.05030, MR 2094802, 10.1017/S0017089504001922 |
| Reference:
|
[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. |
| Reference:
|
[10] Hämäläinen C.: Partitioning $3$-homogeneous latin bitrades.preprint. MR 2390076 |
| Reference:
|
[11] Kirkman T.P.: On a problem of combinations.Cambridge and Dublin Math. J. 2 (1847), 191-204. |
| Reference:
|
[12] Lawrencenko S., Negami S.: Constructing the graphs that triangulate both the torus and the Klein bottle.J. Combin. Theory Ser. B 77 (1999), 211-218. Zbl 1025.05018, MR 1710539, 10.1006/jctb.1999.1920 |
| Reference:
|
[13] Lefevre J.G., Donovan D.M., Grannell M.J., Griggs T.S.: A constraint on the biembedding of Latin squares.submitted. Zbl 1170.05017 |
| Reference:
|
[14] Negami S.: Uniqueness and faithfulness of embedding of toroidal graphs.Discrete Math. 44 (1983), 161-180. Zbl 0508.05033, MR 0689809, 10.1016/0012-365X(83)90057-2 |
| Reference:
|
[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. |
| Reference:
|
[16] White A.T.: Modelling finite geometries on surfaces.Discrete Math. 244 (2002), 479-493. Zbl 0989.05025, MR 1844056, 10.1016/S0012-365X(01)00069-3 |
| . |
