On cross-intersecting families
نویسنده
چکیده
Frankl, P., On cross-intersecting families, Discrete Mathematics 108 (1992) 291-295. Let n 3 t z 1 be integers. Let 9, YI be families of subsets of the n-element set X. They are called cross t-intersecting if IF n GI 2 t holds for all F E 9 and G E 3. If 9 = CfI then 9 is called t-intersecting. Let m(n, t) denote the maximum possible cardinality of a r-intersecting family. Our main result says that if 9, 3 are cross s-intersecting with (31 c ISI ~m(n, t), 1 GS, then 1% + 13) s m(n, 1) + m(n, 2s t) holds and this is best possible.
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