2014/03/05 by Travis Johnston, Linyuan Lu, Johnston, Travis +1
Mathematics · #05C65 #05D05 #05D40 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C65 #msc:05D05 #msc:05D40
paper · pdf · doi:10.48550/arxiv.1403.1220
19 pages
arxiv created 2014/03/05 · arxiv updated 2014/03/06
The hypergraph jump problem and the study of Lagrangians of uniform hypergraphs are two classical areas of study in the extremal graph theory. In this paper, we refine the concept of jumps to strong jumps and consider the analogous problems over non-uniform hypergraphs. Strong jumps have rich topological and algebraic structures. The non-strong-jump values are precisely the densities of the hereditary properties, which include the Turán densities of families of hypergraphs as special cases. Our method uses a generalized Lagrangian for non-uniform hypergraphs. We also classify all strong jump values for \1,2\-hypergraphs.