论文标题
关于定向路径和树木的同态顺序
On the Homomorphism Order of Oriented Paths and Trees
论文作者
论文摘要
如果部分订单包含每个可计数部分订单作为子顺序，则是通用的。在2017年，Fiala，Hubička，Long和NešetêliL表明，图形的同态顺序的每个间隔都是通用的，唯一的例外是微不足道的间隙$ [K_1，K_2] $。我们考虑限于定向路径和树的类别的同态顺序。我们表明，至少4个面向高度的两个方向路径或定向的树之间的每个间隔都是通用的。特殊的间隔是针对方向的路径和树的重合，并包含在形成链条的最多3的定向高度路径中。
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.
