Geodesic
The Sperner property for polygonal graphs
Prikladnaya Diskretnaya Matematika. Supplement, no. 7 (2014), pp. 135-137.

Voir la notice de l'article provenant de la source Math-Net.Ru

A finite partially ordered set (poset) is said to have the Sperner property if at least one of its maximum antichains is formed from elements of the same hight. A polygonal graph is a directed acyclic graph derived from a circuit by some orientation of its edges. The reachability relation of a polygonal graph is a partial order. A criterion is presented for posets associated with polygonal graphs to have the Sperner property.
Keywords: partially ordered set, Sperner property, polygonal graph, path, zigzag. 
@article{PDMA_2014_7_a57,
     author = {V. N. Salii},
     title = {The  {Sperner} property for polygonal graphs},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {135--137},
     publisher = {mathdoc},
     number = {7},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2014_7_a57/}
}
TY  - JOUR
AU  - V. N. Salii
TI  - The  Sperner property for polygonal graphs
JO  - Prikladnaya Diskretnaya Matematika. Supplement
PY  - 2014
SP  - 135
EP  - 137
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDMA_2014_7_a57/
LA  - ru
ID  - PDMA_2014_7_a57
ER  - 
%0 Journal Article
%A V. N. Salii
%T The  Sperner property for polygonal graphs
%J Prikladnaya Diskretnaya Matematika. Supplement
%D 2014
%P 135-137
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDMA_2014_7_a57/
%G ru
%F PDMA_2014_7_a57
V. N. Salii. The  Sperner property for polygonal graphs. Prikladnaya Diskretnaya Matematika. Supplement, no. 7 (2014), pp. 135-137. http://geodesic.mathdoc.fr/item/PDMA_2014_7_a57/

[1] Sperner E., “Ein Satz uber Untermengen einer endlichen Menge”, Math. Zeitschrift., 27:1 (1928), 544–548 | DOI | MR | Zbl

[2] Meshalkin L. D., “Obobschenie teoremy Shpernera o chisle podmnozhestv konechnogo mnozhestva”, Teoriya veroyatnostei i eë primeneniya, 8:2 (1963), 219–220 | Zbl

[3] Stanley E. P., “Weyl groups, the hard Lefschetz theorem and the Sperner property”, SIAM J. Alg. Discr. Math., 1:2 (1980), 168–184 | DOI | MR | Zbl

[4] Wang J., “Proof of a conjecture on the Sperner property of the subgroup lattice of an abelian $p$-group”, Annals Comb., 2:1 (1999), 85–101 | DOI | MR

[5] Jacobson M. S., Kezdy A. E., Seif S., “The poset of connected induced subgraphs of a graph need not be Sperner”, Order, 12:3 (1995), 315–318 | DOI | MR | Zbl

[6] Maeno T., Numata Y., “Sperner property, matroids and finite-dimensional Gorenstein algebras”, Contemp. Math., 280:1 (2012), 73–83 | DOI | MR

[7] Bogomolov A. M., Salii V. N., Algebraicheskie osnovy teorii diskretnykh sistem, Nauka, M., 1997 | MR | Zbl

[8] Salii V. N., “Uporyadochennoe mnozhestvo svyaznykh chastei mnogougolnogo grafa”, Izv. Sarat. un-ta. Nov. cer. Ser. Matematika. Mekhanika. Informatika, 13:2, ch. 2 (2013), 44–51