The Difficulty of Testing for Isomorphism against a Graph That Is Given in Advance
SIAM Journal on Computing
Disjointness Is Hard in the Multi-party Number-on-the-Forehead Model
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
On the minimal density of triangles in graphs
Combinatorics, Probability and Computing
Structure and Randomness: Pages from Year One of a Mathematical Blog
Structure and Randomness: Pages from Year One of a Mathematical Blog
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It is well known 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 close to 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=