On expansive and anti-expansive tree maps
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Date
2018
Authors
Kozerenko, Sergiy
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Journal ISSN
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Abstract
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.
Description
Keywords
maps on trees, Markov graphs, Sharkovsky’s theorem, article
Citation
Kozerenko S. On expansive and anti-expansive tree maps / Sergiy Kozerenko // Opuscula Mathematica. - 2018. - Vol. 38, Issue 3. - P. 379-393.