Counting Bounded Tree Depth Homomorphisms

Martin Grohe

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arXiv · 2003.08164

Counting Bounded Tree Depth Homomorphisms

Martin Grohe

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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'.

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BibTeX RIS

Martin Grohe. 2020-03-18. Counting Bounded Tree Depth Homomorphisms. https://arxiv.org/abs/2003.08164

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