Fractal property of the graph homomorphism order
Combinatorics
2017-05-17 v2 Discrete Mathematics
Abstract
We show that every interval in the homomorphism order of finite undirected graphs is either universal or a gap. Together with density and universality this "fractal" property contributes to the spectacular properties of the homomorphism order. We first show the fractal property by using Sparse Incomparability Lemma and then by more involved elementary argument.
Keywords
Cite
@article{arxiv.1606.07881,
title = {Fractal property of the graph homomorphism order},
author = {Jiří Fiala and Jan Hubička and Yangjing Long and Jaroslav Nešetřil},
journal= {arXiv preprint arXiv:1606.07881},
year = {2017}
}
Comments
8 pages, 5 figures. Minor corrections and reformatting. Accepted to European Journal of Combinatorics