Using Lagrangians of hypergraphs to find non-jumping numbers(II)

Abstract: Let be an integer. A real number is a jump for if for any and any integer , any -uniform graph with vertices and density at least contains a subgraph with vertices and density at least , where does not depend on and . A result of Erdős, Stone and Simonovits implies that every is a jump for . Erdős asked whether the same is true for . Frankl and Rödl gave a negative answer by showing an infinite sequence of non-jumping numbers for every . However, there are a lot of unknowns on determining whether or not a number is a jump for . In this paper, we find two infinite sequences of non-jumping numbers for , and extend one of the results to every . Our approach is still based on the approach developed by Frankl and Rödl. [Copyright &y& Elsevier]