Small length circuits in Eulerian orientations of graphs

Аннотация

In this paper we investigate estimates for number of 3-, 4- and 5-circuits in eulerian tournaments and 4-circuits in eulerian orientations of complete bipartite graphs and hypercubes.
By using obtained relations, we prove uniqueness (up to isomorphism) of orientations, which reach maximum number of 4-circuits in all graph families mentioned above.