On expansive and anti-expansive tree maps

dc.contributor.author	Kozerenko, Sergiy
dc.date.accessioned	2019-05-16T11:55:16Z
dc.date.available	2019-05-16T11:55:16Z
dc.date.issued	2018
dc.description.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.	en_US
dc.identifier.citation	Kozerenko S. On expansive and anti-expansive tree maps / Sergiy Kozerenko // Opuscula Mathematica. - 2018. - Vol. 38, Issue 3. - P. 379-393.	en_US
dc.identifier.issn	1232-9274
dc.identifier.uri	https://ekmair.ukma.edu.ua/handle/123456789/15602
dc.identifier.uri	https://doi.org/10.7494/OpMath.2018.38.3.379
dc.language.iso	en	en_US
dc.relation.source	Opuscula Mathematica. - 2018. - Vol. 38, Issue 3	en_US
dc.status	published earlier	en_US
dc.subject	maps on trees	en_US
dc.subject	Markov graphs	en_US
dc.subject	Sharkovsky’s theorem	en_US
dc.subject	article	en_US
dc.title	On expansive and anti-expansive tree maps	en_US
dc.type	Article	en_US

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