Abstract
Let P be a set of n≥3 points in general position in the plane. The edge disjointness graph D(P) of P is the graph whose vertices are the n2 closed straight line segments with endpoints in P, two of which are adjacent in D(P) if and only if they are disjoint. In this paper we show that the connectivity of D(P) is at most 7n218+Θ(n), and that this upper bound is asymptotically tight. The proof is based on the analysis of the connectivity of D(Qn), where Qn denotes an n-point set that is almost 3-symmetric.
Highlights
We call set in general position to any finite set of points in the Euclidean plane that does not contain three collinear elements
Let P be a set of n ≥ 3 points in general position
Let P be a set of n ≥ 3 points in general positions in the plane
Summary
We call set in general position to any finite set of points in the Euclidean plane that does not contain three collinear elements. Let P be a set of n ≥ 3 points in general position. We recall that a geometric graph is a graph whose vertex set V is a finite set of points in general positions in the plane, and the edges are straight line segments connecting some pairs of V. Let P be a set of n ≥ 3 points in general positions in the plane. In what follows n is an integer with n ≥ 3, and P is an n-point set in general position. We recall that the rectilinear local crossing number of P denoted by lcr( P), is the largest number of crossings on any element of P , and that the rectilinear local crossing number of Kn denoted by lcr(Kn ), is the minimum of lcr( P) taken over all n-point sets P in general position.
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