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Title: | Nonreversible trees having a removable edge | Authors: | MoraΔa, Nenad | Issue Date: | 1-Jan-2018 | Journal: | Filomat | Abstract: | Β© 2018, University of Nis. All rights reserved. A relational structure is said to be reversible iff every bijective homomorphism (condensation) of that structure is an automorphism. In the case of a binary structure π = γX, Ογ, that is equivalent to the following statement: whenever we remove finite or infinite number of edges from π, thus obtaining the structure π β² , we have that π β² β π. In this paper, we prove that if a nonreversible tree π = γX, Ογ has a removable edge (i.e. if there is γx, yγ β Ο such that γX, Ογ β γX, Ο \ {γx, yγ}γ, then it has infinitely many removable edges. We also show that the same is not true for arbitrary binary structure by constructing nonreversible digraphs having exactly n removable edges, for n β β. | URI: | https://open.uns.ac.rs/handle/123456789/1863 | ISSN: | 03545180 | DOI: | 10.2298/FIL1810717M |
Appears in Collections: | PMF Publikacije/Publications |
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