Abstract

In this talk I will describe the ideas behind  1) a new lower bound on  Turan number of 14-cycle, due to A. Terlep and J. Williford;

2)  a new proof for the lower bound on the girth of graphs CD(k, q), due to V. Taranchuk;  3)  a construction of polynomial graphs with small automorphism group and its corollaries, due to V. Taranchuk and myself.  At the end,  several related open questions will be mentioned.