Density and Fractal Property of the Class of Oriented Trees

TL;DR

This paper investigates the structure of finite oriented trees under homomorphism order, proving density and universality of intervals, and explores fractal properties in all finite digraphs.

Contribution

It establishes the density theorem and universality of intervals for finite oriented trees and examines fractal properties in finite digraphs.

Findings

Finite oriented trees are dense under homomorphism order.

Every interval of oriented trees is universal.

Finite digraphs exhibit fractal properties.

Abstract

We show the density theorem for the class of finite oriented trees ordered by the homomorphism order. We also show that every interval of oriented trees, in addition to be dense, is in fact universal. We end by considering the fractal property in the class of all finite digraphs.