Non-jumping densities of 3-uniform hypergraphs
Abstract
A density α∈ [0, 1) is a jump for r if there is some c >0 such that there does not exist a family of r-uniform hypergraphs with Turán density in (α, α+ c). Erdös conjectured that all α∈ [0, 1) are jumps for any r. This was disproven by Frankl and Rödl when they provided examples of non-jumps. In this paper, we provide a method for finding non-jumps for r = 3 using patterns. As a direct consequence, we find a few more examples of non-jumps for r = 3.
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