Fractal property of the graph homomorphism order

Published 25 Jun 2016 in math.CO and cs.DM | (1606.07881v2)

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.

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