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arXiv · 2201.09365

On the Homomorphism Order of Oriented Paths and Trees

Jan Hubička·Jaroslav Nešetřil·Pablo Oviedo·Oriol Serra
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Abstract

A partial order is universal if it contains every countable partial order as a suborder. In 2017, Fiala, Hubička, Long and Nešetřil showed that every interval in the homomorphism order of graphs is universal, with the only exception being the trivial gap $[K_1,K_2]$. We consider the homomorphism order restricted to the class of oriented paths and trees. We show that every interval between two oriented paths or oriented trees of height at least 4 is universal. The exceptional intervals coincide for oriented paths and trees and are contained in the class of oriented paths of height at most 3, which forms a chain.

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Jan Hubička, Jaroslav Nešetřil, Pablo Oviedo, Oriol Serra. 2022-01-25. On the Homomorphism Order of Oriented Paths and Trees. https://doi.org/10.1007/978-3-030-83823-2_118

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