Improved bounds on the extremal function of hypergraphs [article]

William Zhang
2018 arXiv   pre-print
A fundamental problem in pattern avoidance is describing the asymptotic behavior of the extremal function and its generalizations. We prove an equivalence between the asymptotics of the graph extremal function for a class of bipartite graphs and the asymptotics of the matrix extremal function. We use the equivalence to prove several new bounds on the extremal functions of graphs. We develop a new method to bound the extremal function of hypergraphs in terms of the extremal function of their
more » ... ciated multidimensional matrices, improving the bound of the extremal function of d-permutation hypergraphs of length k from O(n^d-1) to 2^O(k)n^d-1.
arXiv:1807.02411v1 fatcat:igfsh4pzg5g2zj27hvwvmqgx2u