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比利时vs摩洛哥足彩
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比利时vs摩洛哥足彩
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university of california san diego
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combinatorics seminar (math 269)
sam spiro
rutgers university
clique and berge supersaturation for $k_{2,t}$.
abstract:
a famous conjecture of erd\h{o}s and simonovits says that if $g$ is an $n$ vertex graph with much more than $\ex(n,f)$ edges, then $g$ contains about as many copies of $f$ as the random graph of the same density. in this talk we show that several natural generalizations of this conjecture fails to be true. in particular, we show that for large $t$, there exist $n$ vertex graphs with $\theta(kn^{3/2})$ triangles such that $g$ contains a total of $k^tn^{3/2+o(1)}$ copies of $k_{2,t}$ (with the random graph of the same triangle density containing $\theta(k^{2t/3}n^2)$ copies), and we show that this bound is essentially best possible for $k\le n^{1/2t}$. our constructions rely on solving certain unbalanced bipartite tur\'an problems using random polynomial graphs. this is joint work with quentin dubroff, benjamin gunby, and bhargav narayanan.
host: brendon rhoades
may 9, 2023
4:00 pm
apm 6402
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