The Szemer\'edi-Petruska conjecture for a few small values
Abstract
Let H be a 3-uniform hypergraph of order n with clique number k such that the intersection of all maximum cliques of H is empty. For fixed m=n-k, Szemer\'edi and Petruska conjectured the sharp bound n≤ m+2 2. In this note the conjecture is verified for m=2,3 and 4.
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