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{\bf Andrew Suk}
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{\bf A Note on $K_{k,k}$-Cross Free Families}
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We give a short proof that for any fixed integer $k$, the maximum
number size of a $K_{k,k}$-cross free family is linear in the size of
the groundset.  We also give tight bounds on the maximum size of a
$K_k$-cross free family in the case when ${\cal F}$ is intersecting
or an antichain.



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