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A cluster in a drawing of a graph in the plane is the set of four endpoints of the two edges involved in a crossing. A independent drawing is a drawing in which the clusters are pairwise disjoint. Albertson [1] asked for the maximum k such that every independent drawing with k crossings has an independent set consisting of one vertex from each cluster. We(More)
A sequence of nonnegative integers π is graphic if it is the degree sequence of some graph G. In this case we say that G is a realization of π, and we write π = π(G). A graphic sequence π is potentially H-graphic if there is a realization of π that contains H as a subgraph. that π 1 majorizes π 2 if d i ≥ s i for all i, 1 ≤ i ≤ n. In 1970, Erd˝ os showed(More)