Given an in…nite hereditary property of graphs P; the principal extremal parameter of P is the value (P) = lim n!1 n 2 1 maxfe (G) : G 2 P and v (G) = ng: The Erd1⁄2os-Stone theorem gives (P) if P is monotone, but this result does not apply to hereditary P. Thus, one of the results of this note is to establish (P) for any hereditary property P: Similar questions are studied for the parameter (p...

In standard property testing, the task is to distinguish between objects that have a property P and those that are ε-far from P , for some ε > 0. In this setting, it is perfectly acceptable for the tester to provide a negative answer for every input object that does not satisfy P . This implies that property testing in and of itself cannot be expected to yield any information whatsoever about t...

We study constructions of k×n matrices A that both (1) satisfy the restricted isometry property (RIP) at sparsity s with optimal parameters, and (2) are efficient in the sense that only O(n log n) operations are required to compute Ax given a vector x. Our construction is based on repeated application of independent transformations of the form DH , where H is a Hadamard or Fourier transform and...

in this paper‎, ‎we investigate the influence of some subgroups of sylow subgroups with semi cover-avoiding property and‎ ‎$mathcal{f}$-supplementation on the structure of finite groups and generalize a series of known results‎.