Algebra and Combinatorics Seminar

Date: September 17, 2021

Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: Chun-Hung Liu, TAMU

Title: Homomorphism counts in robustly sparse graphs

Abstract: For a fixed graph H and for arbitrarily large host graphs G, the number of homomorphisms from H to G and the number of subgraphs isomorphic to H contained in G have been extensively studied in extremal graph theory and graph limits theory when the host graphs are allowed to be dense. This talk addresses the case when the host graphs are robustly sparse and proves a general theorem that solves a number of open questions proposed since 1990s and strengthens a number of results in the literature. In particular, our result determines, up to a constant multiplicative error, the maximum number of subgraphs isomorphic to H of an n-vertex graph in any fixed class of graphs with bounded expansion, which applies to any (topological) minor-closed family and many graph classes with certain geometric properties.