Geodesic
The Sperner property for trees
Prikladnaya Diskretnaya Matematika. Supplement, no. 8 (2015), pp. 124-127.

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

The reachability relation of a directed acyclic graph is a partial order on the set of its vertices. One of the interesting properties of a partially ordered set is its Sperner property that means that at least one of maximum antichains is formed from elements of the same height. In graphs with the reachability relation, this property is discussed for out-trees and in-trees, it is modified and studied for functional and contrafunctional digraphs closely related to these trees, and for unoriented trees also.
Keywords: partially ordered set, Sperner property, tree, acyclic digraph, out-tree, in-tree, functional digraph, contrafunctional digraph. 
@article{PDMA_2015_8_a46,
     author = {V. N. Salii},
     title = {The {Sperner} property for trees},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {124--127},
     publisher = {mathdoc},
     number = {8},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2015_8_a46/}
}
TY  - JOUR
AU  - V. N. Salii
TI  - The Sperner property for trees
JO  - Prikladnaya Diskretnaya Matematika. Supplement
PY  - 2015
SP  - 124
EP  - 127
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDMA_2015_8_a46/
LA  - ru
ID  - PDMA_2015_8_a46
ER  - 
%0 Journal Article
%A V. N. Salii
%T The Sperner property for trees
%J Prikladnaya Diskretnaya Matematika. Supplement
%D 2015
%P 124-127
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDMA_2015_8_a46/
%G ru
%F PDMA_2015_8_a46
V. N. Salii. The Sperner property for trees. Prikladnaya Diskretnaya Matematika. Supplement, no. 8 (2015), pp. 124-127. http://geodesic.mathdoc.fr/item/PDMA_2015_8_a46/

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

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

[3] Salii V. N., “Shpernerovo svoistvo dlya mnogougolnykh grafov”, Prikladnaya diskretnaya matematika. Prilozhenie, 2014, no. 7, 135–137

[4] Novokshonova E. N., “Shpernerovo svoistvo dlya lineinykh grafov”, Kompyuternye nauki i informatsionnye tekhnologii, Materialy Mezhdunar. nauch. konf., Izdat. Tsentr “Nauka”, Saratov, 2014, 230–231

[5] Atkinson M. D., Ng D. T. N., “On the width of an orientation of a tree”, Order, 5:1 (1988), 33–43 | DOI | MR | Zbl

[6] Kharari F., Teoriya grafov, Mir, M., 1973 | MR