Bond paths, local energy density properties, and Laplacian, L(r) = -wedge(2)rho(r), composite isosurfaces of the electron density distributions were calculated for the intramolecular and intermolecular bonded interactions for molecular solids of As(2)O(3) and AsO(2) composition, an As(2)O(5) crystal, a number of arsenate molecules, and the arsenic metalloid, arsenolamprite. The directed intermo...

We call the digraph D an m-coloured digraph if the arcs of D are coloured with m colours. A directed path (or a directed cycle) is called monochromatic if all of its arcs are coloured alike. A set N ⊆ V (D) is said to be a kernel by monochromatic paths if it satis5es the following two conditions: (i) For every pair of di7erent vertices u, v∈N , there is no monochromatic directed path between th...

The quest for colorful components (connected components where each color is associated with at most one vertex) inside a vertex-colored graph has been widely considered in the last ten years. Here we consider two variants, Minimum Colorful Components (MCC) and Maximum Edges in transitive Closure (MEC), introduced in the context of orthology gene identification in bioinformatics. The input of bo...

The NP-hard Colorful Components problem is, given a vertex-colored graph, to delete a minimum number of edges such that no connected component contains two vertices of the same color. It has applications in multiple sequence alignment and in multiple network alignment where the colors correspond to species. We initiate a systematic complexity-theoretic study of Colorful Components by presenting...

Disjoint Paths is the problem of finding paths between given pairs of terminals in a graph such that no vertices are shared between paths. We analyze fixed-parameter tractability of several new Disjoint Paths-like routing problems motivated by congestion control in computer networks. In one model we are interested in finding paths between k pairs of terminals such that the first edge of each pa...

We provide a simple linear time transformation from a directed or undirected graph with labeled edges to an unlabeled digraph, such that paths in the input graph in which no two consecutive edges have the same label correspond to paths in the transformed graph and vice versa. Using this transformation, we provide efficient algorithms for finding paths and cycles with no two consecutive equal la...

The shortest paths problem on weighted directed graphs is one of the basic network optimization problems. Its importance is mainly due to its applications in various areas, such as communication and transportation. Given a source node s in a weighted directed graph G, with n nodes and m arcs, the single-source shortest path problem (SSSP, for short) from s is the problem of finding the minimum ...