What paths have length?

Paths of length four

Maximal Length Common Non-intersecting Paths

Given a set P n of n points on the plane labeled with the integers f1; : : : ; ng, an increasing path of P n is a sequence of points i 1 < : : : < i k such that the polygonal path ob-1 is non-self intersecting. We show that any point set on the plane admits an increasing path of length at least p 2n. We also study the problem of nding the longest common increasing path of two convex point sets ...

Packing paths of length at least two

We give a simple proof for Kaneko’s theorem which gives a su2cient and necessary condition for the existence of vertex disjoint paths in a graph, each of length at least two, that altogether cover all vertices of the original graph. Moreover we generalize this theorem and give a formula for the maximum number of vertices that can be covered by such a path system. c © 2004 Elsevier B.V. All righ...

Length-bounded disjoint paths in planar graphs

Efficiently Listing Bounded Length st-Paths

The problem of listing the K shortest simple (loopless) stpaths in a graph has been studied since the early 1960s. For a nonnegatively weighted graph with n vertices and m edges, the most efficient solution is an O(K(mn+n log n)) algorithm for directed graphs by Yen and Lawler [Management Science, 1971 and 1972], and an O(K(m+ n log n)) algorithm for the undirected version by Katoh et al. [Netw...