K_(2,t+1)-free graphs with many copies of K_(t,t)
classification
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copiesfreeanswersargumentcombinedconstructcontainingcounting
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For every fixed integer $t\geq 3$, we construct an $n$-vertex $K_{2,t+1}$-free graph containing $\Omega_t(n^2)$ copies of $K_{t,t}$. Combined with a simple counting argument, this shows that \[ \mathrm{ex}(n,K_{t,t},K_{2,t+1})=\Theta_t(n^2). \] This answers a question of Spiro.
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Forward citations
Cited by 2 Pith papers
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On the generalized Tur\'an number of complete bipartite graphs
Proves ex(n, K_{a,b}, K_{s,t}) = Theta(n^s) for s in {2,3} with s < a <= b and t large, plus existence of infinitely many r with ex(n, F, H) = Theta(n^r) for any edge-containing F.
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$K_{2, t+1}$-free graphs containing an optimal number of $K_{t, t}$'s
For prime power t and n = t^{2e-1}, ex(n, K_{t,t}, K_{2,t+1}) = (1 + o(1)) n² / (2t(t-1)).
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