On the Homomorphism Order of Oriented Paths and Trees
arXiv:2201.09365 · doi:10.1007/978-3-030-83823-2_118
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 . 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.
6 pages, 1 figure. Extended abstract for Eurocomb 2021; corrected title