Recent trends and future directions in vertex-transitive graphs

A graph is said to be vertex-transitive if its automorphism group acts transitively on the vertex set. Some recent developments and possible future directions regarding two famous open problems, asking about existence of Hamilton paths and existence of semiregular automorphisms in vertex-transitive graphs, are discussed, together with some recent results on arc-transitive graphs and half-arc-transitive graphs, two special classes of vertex-transitive graphs that have received particular attention over the last decade

Configurations and graphs—II

AbstractThe aim of this paper is to give a second survey on relations between graphs and configurations in the sense of [10]. It contains some further relations as well as additional remarks to topics which were mentioned in the first survey. In particular, a new and quite general connection concerning the existence of certain configurations and the blocking set property is described. Since the relations between graphs and configurations are also important from a historical point of view the last part contains some historical facts and some general background of the history of configurations