The spread of Kn Original Research Article

Given an Euler tour t of G let the spread(t) of the tour t be the minimum distance along the tour between two repetitions of the same vertex. Let G be an Eulerian graph and let the spread of G spread(G) be the maximum value of spread(t) over all Euler tours t of G. In this paper we give some bounds for spread(Kn) for certain integers n. For instance, it is shown that spread(K4m+1) ⩾ 2m − 1.