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- W3184416441 abstract "In this note, we give short proofs of three theorems about intersection problems. The first one is a determination of the maximum size of a nontrivial $k$-uniform, $d$-wise intersecting family for $nge left(1+frac{d}{2}right)(k-d+2)$, which improves upon a recent result of O'Neill and Verstraete. Our proof also extends to $d$-wise, $t$-intersecting families, and from this result we obtain a version of the Erdős-Ko-Rado theorem for $d$-wise, $t$-intersecting families. The second result partially proves a conjecture of Frankl and Tokushige about $k$-uniform families with restricted pairwise intersection sizes. The third result concerns graph intersections. Answering a question of Ellis, we construct $K_{s, t}$-intersecting families of graphs which have size larger than the Erdős-Ko-Rado-type construction whenever $t$ is sufficiently large in terms of $s$." @default.
- W3184416441 created "2021-08-02" @default.
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- W3184416441 date "2021-04-01" @default.
- W3184416441 modified "2023-09-27" @default.
- W3184416441 title "Short proofs of three results about intersecting systems" @default.
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