| On the Density of a Graph and its Blowup (2009) | |||||||||
Abstract | |||||||||
| The theorem of Chung, Graham, and Wilson on quasi-random graphs asserts that of all graphs with edge density p, the random graph G(n,p) contains the smallest density of copies of K_{t,t}, the complete bipartite graph of size 2t. Since K_{t,t} is a t-blowup of an edge, the following intriguing open question arises: Is it true that of all graphs with triangle density p^3, the random graph G(n,p) contains the smallest density of K_{t,t,t}, which is the t-blowup of a triangle? Our main result gives an indication that the answer to the above question is positive by showing that for some blowup, the answer must be positive. More formally we prove that if G has triangle density p^3, then there is some 2 | |||||||||
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