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ArticleSaumell, MariaLet P be a set of n points in the plane. A geometric proximity graph on P is a graph where two points are connected by a straightline segment if they satisfy some prescribed proximity rule. We consider four classes of higher order proximity graphs, n . . .

ArticleFernandez, SilviaWe give a new upper bound for the rectilinear crossing number of the complete geometric graph . We prove that by means of a new construction based on an iterative duplication strategy starting with a set having a certain structure of halving lines.

ArticleSacristán, VeraLet P be a set of n points in the plane. A geometric proximity graph on P is a graph where two points are connected by a straightline segment if they satisfy some prescribed proximity rule. We consider four classes of higher order proximity graphs, n . . .

ArticleSalazar, GelasioThe Harary–Hill Conjecture states that the number of crossings in any drawing of the complete graph KnKn in the plane is at least Z(n):=14⌊n2⌋⌊n−12⌋⌊n−22⌋⌊n−32⌋Z(n):=14⌊n2⌋⌊n−12⌋⌊n−22⌋⌊n−32⌋. In this paper, we settle the Harary–Hill conjecture for she . . .