比利时vs摩洛哥足彩
,
university of california san diego
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math 269 - seminar in combinatorics
ji zeng
alfréd rényi institute of mathematics, budapest (jzeng@ucsd.edu)
unbalanced zarankiewicz problem for bipartite subdivisions
abstract:
a real number $\sigma$ is called a \textit{linear threshold} of a bipartite graph $h$ if every bipartite graph $g = (u \sqcup v, e)$ with unbalanced parts $|v| \gtrsim |u|^\sigma$ and without a copy of $h$ must have a linear number of edges $|e| \lesssim |v|$. we prove that $\sigma_s = 2 - 1/s$ is a linear threshold of the \textit{complete bipartite subdivision} graph $k_{s,t}'$. moreover, we show that any $\sigma < \sigma_s$ is not a linear threshold of $k_{s,t}'$ for sufficiently large $t$ (depending on $s$ and $\sigma$). some applications of our result in incidence geometry are discussed.
lutz warnke
october 22, 2024
2:00 pm
ap&m 7321
research areas
combinatorics****************************
