## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

 Mittagsseminar Talk Information

Date and Time: Tuesday, December 05, 2017, 12:15 pm

Duration: 45 minutes

Location: CAB G51

Speaker: Aleksandr Efremov

## Homomorphisms Are a Good Basis for Counting Small Subgraphs

We will present how the problem of counting subgraphs can be reduced to the problem of counting homomorphisms. Based on that, we will show how to count subgraph copies of k-edge pattern in n-vertex host in time $k^{O(k)} \cdot n^{0.174k + o(k)}$. Relations between counting subraphs, induced subgraphs and homomorphisms and complexity of these problems will be discussed. Main part of the talk is based on the results of the paper by Curticapean, Dell, Marx from 2017.

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