Leírás
Abstract. Let us call a simple graph on n>1 vertices a prime gap graph if its vertex degrees are 1 and the first n-1 prime gaps (we need the 1 so that the sum of these numbers is even). We can show that such a graph exists for every large n, and under RH for every n>1. Moreover, a sequence of such graphs can be generated by a so-called degree preserving growth process: in any prime gap graph on n vertices, we can find (p_{n+1}-p_n)/2 independent edges, delete them, and connect the ends to a new, (n+1)-th vertex. This creates a prime gap graph on n+1 vertices, and the process never ends. Joint work with P. L. Erdős, S. R. Kharel, P. Maga, T. R. Mezei, and Z. Toroczkai. The talk will be in Hungarian, but the slides will be in English.
For Zoom access please contact Andras Biro (biro.andras[a]renyi.hu).