We show that for each fixed k, the problem of finding k pairwise vertex-disjoint directed paths between given pairs of terminals in a directed planar graph is solvable in polynomial time.

By using the probabilistic method, we show that the maximum number of directed Hamiltonian paths in a complete directed graph with n vertices is at least (e− o(1)) n! 2n−1 .

We discuss various aspects of the randomly interacting directed polymers with emphasis on the phases and phase transition. We also discuss the behaviour of overlaps of directed paths in a random medium. Typeset using REVTEX

Several authors have studied convergence in distribution to the Brownian web under diffusive scaling of systems Markovian random walks. In a paper by R. Roy, K. Saha and A. Sarkar, is proved for system coalescing paths—the directed forest—which are not Markovian. Paths forest do cross each other before coalescence. Here, we study variation where paths can prove web. This provides an example how...

Higher Dimensional Automata (HDA) are higher dimensional relatives to transition systems in concurrency theory taking into account which degree various actions commute. Mathematically, they take the form of labelled cubical complexes. It is important know, and challenging from a geometric/topological perspective, whether space directed paths (executions model) between two vertices (states) conn...