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Problem 1
Let Fϲ 2[n] be a family whose members are all sets of size 4, such that any set {a,b,c} C [n] of three elements is contained in exactly one member of F. Show that n Ξ2 or 4 (mod 6).
Problem 2
Let K¯4 be the graph formed by removing one edge from K4 (up to isomorphism there is only one such graph K¯4). Let p = p(n) be a sequence of numbers between 0 and 1. Show that if n⁴p⁵ -> 0 then w.h.p. G(n,p) does not contain K¯4 as a subgraph. Then show that if n⁴p⁵ -> oc then w.h.p. G(n.p) does contain K¯4 as a subgraph.

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Combinatorics Questions
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