2 research outputs found
Three Edge-disjoint Plane Spanning Paths in a Point Set
We study the following problem: Given a set of points in the plane,
how many edge-disjoint plane straight-line spanning paths of can one draw?
A well known result is that when the points are in convex position,
such paths always exist, but when the points of are in
general position the only known construction gives rise to two edge-disjoint
plane straight-line spanning paths. In this paper, we show that for any set
of at least ten points, no three of which are collinear, one can draw at least
three edge-disjoint plane straight-line spanning paths of~. Our proof is
based on a structural theorem on halving lines of point configurations and a
strengthening of the theorem about two spanning paths, which we find
interesting in its own right: if has at least six points, and we prescribe
any two points on the boundary of its convex hull, then the set contains two
edge-disjoint plane spanning paths starting at the prescribed points.Comment: Appears in the Proceedings of the 31st International Symposium on
Graph Drawing and Network Visualization (GD 2023