Geodesic
On the number of Sperner vertices in a~tree
Prikladnaâ diskretnaâ matematika, no. 2 (2016), pp. 115-118.

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A vertex $v$ of a tree $T$ is called a Sperner vertex if the in-tree $T(v)$ obtained from $T$ by orientation of all edges towards $v$ has the Sperner property, i.e. there exists a largest subset $A$ of mutually unreachable vertices in it such that all vertices in $A$ are equidistant to $v$. Some explicit methods to count the number of Sperner vertices in certain special trees are presented.
Keywords: graph, path, star, palm-tree, rank, caterpillar, train of palm-trees.
Mots-clés : Sperner vertex 
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V. N. Salii. On the number of Sperner vertices in a~tree. Prikladnaâ diskretnaâ matematika, no. 2 (2016), pp. 115-118. http://geodesic.mathdoc.fr/item/PDM_2016_2_a7/

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

[2] Saliy V. N., “The Sperner property for polygonal graphs”, Prikladnaya diskretnaya matematika. Prilozhenie, 2014, no. 7, 135–137 (in Russian)

[3] Saliy V. N., “The Sperner property for trees”, Prikladnaya diskretnaya matematika. Prilozhenie, 2015, no. 8, 124–127 (in Russian)