A proof of the rooted tree alternative conjecture
classification
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keywords
conjecturetreesrootedtreealternativeanaloguebonatoclasses
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Bonato and Tardif conjectured that the number of isomorphism classes of trees mutually embeddable with a given tree T is either 1 or infinite. We prove the analogue of their conjecture for rooted trees. We also discuss the original conjecture for locally finite trees and state some new conjectures.
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