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This paper proposes a general framework to study the conflict resolution for multiple intersecting flows of aircraft in planar airspace. The conflict-resolution problem is decomposed into a sequence of subproblems, each involving only two intersecting flows of aircraft. The strategy for achieving the decomposition is to laterally displace the aircraft flows so that they intersect in pairs, and the resulting conflict zones have no overlap. A conflict zone is defined as a circular area that is centered at the intersection of a pair of flows, which allows aircraft approaching the intersection to resolve the conflict completely within the conflict zone without straying outside. An optimization problem is then formulated to minimize the lateral displacements of the aircraft flows. Although this optimization problem is difficult to solve in general due to its nonconvex nature, a closed-form solution can be obtained for three intersecting flows. The minimum requirement of lateral displacements of aircraft flows for conflict resolution can also be used as a metric of traffic complexity for multiple intersecting flows of aircraft. It is shown that the order of growth of this complexity metric is O(n 3) for symmetric configurations of n flows of aircraft.