比利时vs摩洛哥足彩
,
university of california san diego
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math 269 - combinatorics seminar
michael tait
carnegie mellon university (cmu)
on the tur\'an number of theta graphs
abstract:
the theta graph $\theta_{k, t}$ consists of two vertices with $t$ internally disjoint paths of length $k$ between them. since $\theta_{k,2}$ is a cycle of length $2k$, the study of the tur\'an number of this graph includes the notorious even-cycle problem. we show that for fixed $k$ and large $t$, a graph without a $\theta_{k,t}$ contains at most $c_k t^{1-1/k}n^{1+1/k}$ edges, and we use graphs constructed via random polynomials to show that this is sharp up to the constant $c_k$ when $k$ is odd.
host: jacques verstraete
may 17, 2018
3:00 pm
ap&m 6218
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