A proof of Jean de Rumeurʹs conjecture Original Research Article

We give an elementary proof of Jean de Rumeurʹs conjecture stating that in any digraph G of diameter D, such that the sum of the indegree and outdegree of every vertex is at most 2d, the number of vertices is at most 1 + d + d2 + … + dD. Our result implies that known good solutions in the case d + = d − = d are also quasi-optimal under the assumption that d + + d− = 2d.