On expansive and anti-expansive tree maps

• Autorzy: Kozerenko S

Identyfikatory

DOI

10.7494/OpMath.2018.38.3.379

• Języki publikacji: EN

Abstrakty

EN

With every self-map on the vertex set of a finite tree one can associate the directed graph of a special type which is called the Markov graph. Expansive and anti-expansive tree maps are two extremal classes of maps with respect to the number of loops in their Markov graphs. In this paper we prove that a tree with at least two vertices has a perfect matching if and only if it admits an expansive cyclic permutation of its vertices. Also, we show that for every tree with at least three vertices there exists an expansive map with a weakly connected (strongly connected provided the tree has a perfect matching) Markov graph as well as anti-expansive map with a strongly connected Markov graph.

Słowa kluczowe

EN

maps on trees; Markov graphs; Sharkovsky's theorem

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2018
• Tom: Vol. 38, no. 3
• Strony: 379--393
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Kozerenko S

• Taras Shevchenko National University of Kyiv Faculty of Mechanics and Mathematics Volodymyrska Str. 64, 01033 Kyiv, Ukraine

Bibliografia

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• [12] M. Tchuente, Parallel realization of permutations over trees, Discrete Math. 39 (1982), 211-214.
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Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).