Using graph concepts to assess the feasibility of a sequenced air traffic flow with low conflict rate

In this paper, we propose to study feasibility issues of a new air traffic paradigm. In this paradigm, aircraft are following immaterial moving points in such a way that no conflict (or at most few) occurs between aircraft. We provide lower and upper bounds on the maximum density of a solution. In particular, we characterize the density of the solution according to the colorability of an auxiliary graph, modelling the potential conflicts between moving points.