# Online Talk: Chun-Hung Liu

Tuesday, Feb 15, 4pm ET (9pm GMT, 10am Wed NZDT)
Chun-Hung Liu, Texas A&M University
Homomorphism counts in robustly sparse graphs

##### For a fixed graph $H$ and for arbitrarily large host graphs $G$, the numberof homomorphisms from $H$ to $G$ and the number of subgraphs isomorphic to $H$contained in $G$ have been extensively studied when the host graphs areallowed to be dense. This talk addresses the case when the host graphsare robustly sparse. We determine, up to a constant multiplicativeerror, the maximum number of subgraphs isomorphic to $H$ contained in an$n$-vertex graph in any fixed hereditary graph class with boundedexpansion. This result solves a number of open questions and can begeneralized to counting the number of homomorphisms.

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