The Szemerédi–Petruska conjecture for a few small values
The Szemerédi–Petruska conjecture for a few small values
Abstract Let H be a 3-uniform hypergraph of order n with clique number $$\omega (H)=k$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ω</mml:mi> <mml:mo>(</mml:mo> <mml:mi>H</mml:mi> <mml:mo>)</mml:mo> <mml:mo>=</mml:mo> <mml:mi>k</mml:mi> </mml:mrow> </mml:math> . Assume that the union of the k -cliques of H equals its vertex set, the intersection of all maximum cliques of H is …