Papers › A note on estimating global subgraph counts by sampling
A note on estimating global subgraph counts by sampling
Svante Janson, Valentas Kurauskas
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We give a simple proof of a generalization of an inequality for homomorphism counts by Sidorenko (1994). A special case of our inequality says that if dᵥ denotes the degree of a vertex v in a graph G and Hom_Δ(H, G) denotes the number of homomorphisms from a connected graph H on h vertices to G which map a particular vertex of H to a vertex v in G with dᵥ ≥Δ, then Hom_Δ(H,G) ≤∑_(v∈G) dᵥʰ⁻¹1_(dᵥ≥Δ) We use this inequality to study the minimum sample size needed to estimate the number of copies of H in G by sampling vertices of G at random.
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