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 
@article{PDM_2016_2_a7,
     author = {V. N. Salii},
     title = {On the number of {Sperner} vertices in a~tree},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {115--118},
     publisher = {mathdoc},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2016_2_a7/}
}
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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/