Counting Bounded Tree Depth Homomorphisms
Logic in Computer Science
2020-03-19 v1 Discrete Mathematics
Combinatorics
Abstract
We prove that graphs G, G' satisfy the same sentences of first-order logic with counting of quantifier rank at most k if and only if they are homomorphism-indistinguishable over the class of all graphs of tree depth at most k. Here G, G' are homomorphism-indistinguishable over a class C of graphs if for each graph F in C, the number of homomorphisms from F to G equals the number of homomorphisms from F to G'.
Keywords
Cite
@article{arxiv.2003.08164,
title = {Counting Bounded Tree Depth Homomorphisms},
author = {Martin Grohe},
journal= {arXiv preprint arXiv:2003.08164},
year = {2020}
}