| Title:
|
On centrally symmetric graphs (English) |
| Author:
|
Stern, Manfred |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
121 |
| Issue:
|
1 |
| Year:
|
1996 |
| Pages:
|
25-28 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this note we extend results on the covering graphs of modular lattices (Zelinka) and semimodular lattices (Gedeonova, Duffus and Rival) to the covering graph of certain graded lattices. (English) |
| Keyword:
|
covering graph |
| Keyword:
|
symmetric graph |
| Keyword:
|
centrally symmetric lattice |
| Keyword:
|
graded lattice |
| Keyword:
|
strong lattice |
| Keyword:
|
semimodular lattice |
| MSC:
|
05C75 |
| MSC:
|
05C99 |
| MSC:
|
06B05 |
| MSC:
|
06C10 |
| MSC:
|
06E05 |
| idZBL:
|
Zbl 0863.06009 |
| idMR:
|
MR1388170 |
| DOI:
|
10.21136/MB.1996.125944 |
| . |
| Date available:
|
2009-09-24T21:14:38Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125944 |
| . |
| Reference:
|
[1] P. Crawley, R. P. Dilworth: Algebraic Theory of Lattices.Prentice Hall, Englewood Cliffs, New Jersey, 1973. Zbl 0494.06001 |
| Reference:
|
[2] D. Duffus, I. Rival: Path length in the covering graph of a lattice.Discrete Math. 19 (1977), 139-158. Zbl 0372.06005, MR 0543829, 10.1016/0012-365X(77)90029-2 |
| Reference:
|
[3] U. Faigle: Geometries on partially ordered sets.J. Combin. Theory Ser. B 28 (1977), 26-51. MR 0565509, 10.1016/0095-8956(80)90054-4 |
| Reference:
|
[4] E. Gedeonová: Lattices whose covering graphs are S-graphs.Colloq. Math. Soc. János Bolyai 33 (1980), 407-435. MR 0724274 |
| Reference:
|
[5] E. Gedeonová: Lattices with centrally symmetric covering graphs.Proc. Klagenfurt Conf. June 10-13, 1982, Contributions to General Algebra 2. Verlag Hölder-Pichler-Tempsky, Wien, 1983, pp. 107-113. MR 0721649 |
| Reference:
|
[6] G. Grätzer: General Lattice Theory.Birkhäuser Verlag, Basel, 1978. MR 0504338 |
| Reference:
|
[7] A. Kotzig: Centrally symmetric graphs.Czechoslovak Math. J. 18 (1968), 606-615. (In Russian.) MR 0237376 |
| Reference:
|
[8] J. P. S. Kung: Matchings and Radon transforms in lattices, I. Consistent lattices.Order 2, 105-112. Zbl 0582.06008, MR 0815856, 10.1007/BF00334848 |
| Reference:
|
[9] K. Reuter: The Kurosh-Ore exchange property.Acta Math. Hung. 53, 119-127. Zbl 0675.06003, MR 0987044, 10.1007/BF02170062 |
| Reference:
|
[10] M. Stern: Semimodular Lattices.B.G.Teubner Verlagsgesellschaft, Stuttgart und Leipzig, 1991. Zbl 0743.06008, MR 1164868 |
| Reference:
|
[11] M. Stern: Dually atomistic lattices.Discrete Math. 93 (1991), 97-100. Zbl 0759.06006, MR 1141266, 10.1016/0012-365X(91)90220-V |
| Reference:
|
[12] B. Zelinka: Centrally symmetric Hasse diagrams of finite modular lattices.Czechoslovak Math. J. 20 (1970), 81-83. Zbl 0194.32601, MR 0255441 |
| . |
