In the minimum path coloring problem, we are given a graph and a set of pairs of vertices of the graph and we are asked to connect the pairs by colored paths in such a way that pa...
It is shown that for a set S of n pairwise disjoint axis-parallel line segments in the plane there is a simple alternating path of length ( n). This bound is best possible in the...
Let B be a set of n arbitrary possibly intersecting convex obstacles in Rd. It is shown that any two points which can be connected by a path avoiding the obstacles can also be c...
The disjoint paths problem asks, given an graph G and k + 1 pairs of terminals (s0, t0), . . . , (sk, tk), whether there are k + 1 pairwise disjoint paths P0, . . . , Pk, such tha...
We study the parameterized complexity of two families of problems: the bounded length disjoint paths problem and the bounded length cut problem. From Menger’s theorem both proble...