Let G(V; E) be a graph (either directed or undirected) with a non-negative length`(e) associated with each arc e in E. For two speciied nodes s and t in V , the k most vital arcs (or nodes) are those k arcs (nodes) whose removal maximizes the increase in the length of the shortest path from s to t. We prove that nding the k most vital arcs (or nodes) is NP-hard, even when all arcs have unit len...

The paper considers a generalization of the well known random placement of balls into bins. Given n circular arcs of lengths 1, : : : ,n we study the maximum number of overlapping arcs on a circle if the starting points of the arcs are chosen randomly. We give almost exact tail bounds on the maximum overlap of the arcs. These tail bounds yield a characterization of the expected maximum overlap ...

We classify the arcs in PG(2, q), q odd, which consist of (q + 3)/2 points of a conic C and two points not on te conic but external to C, or (q + 1)/2 points of C and two additional points, at least one of which is an internal point of C. We prove that for arcs of the latter type, the number of points internal to C can be at most 4, and we give a complete classification of all arcs that attain ...

By using a magnetosphere-ionosphere (M-I) coupling model of polar cap arcs [Zhu et al., 1993], a systematic model study of the effects of ionospheric background conductivity on the formation of polar cap arcs has been conducted. The variations of the ionospheric background conductivity in the model study cover typical ionospheric onditions, including solar minimum, solar maximum, winter, and su...

In this paper, we generalize a result by Ball, Hill, Landjev and Ward on plane arcs to arcs with multiple points in spaces of arbitrary dimension. This result is further applied to the characterization of some non-Griesmer arcs in the 3-dimensional projective geometry over F4.

We show that doubling, linearly connected metric spaces are quasiarc connected. This gives a new and short proof of a theorem of Tukia.