Abstract: Dragan Marušič

LOOKING BACK AND AHEAD: THREE OPEN PROBLEMS IN VERTEX-TRANSITIVE GRAPHS

 

           We will give a short overview and discuss possible future directions with regards to the following long standing open problems:

                      (i) existence of semiregular automorphisms in vertex-transitive graphs;
                      (ii) existence of Hamilton cycles in Cvertex-transitive and Cayley graphs; and
                      (iii) existence of strongly regular bicirculants and their relation, in particular, to primitive groups of degree twice an odd prime.