A systematic, language-independent method of finding a minimal set of paths covering the code of a sequential program is proposed for application in White Box testing. Execution of all paths from the set ensures also statement coverage. Execution fault marks problematic areas of the code. The method starts from a UML activity diagram of a program. The diagram is transformed into a directed grap...

Fine-grained reductions have established equivalences between many core problems with Õ(n3)-time algorithms on n-node weighted graphs, such as Shortest Cycle, All-Pairs Shortest Paths (APSP), Radius, Replacement Paths, Second Shortest Paths, and so on. These problems also have Õ(mn)-time algorithms on m-edge n-node weighted graphs, and such algorithms have wider applicability. Are these mn boun...

This paper addresses the natural relaxation of the path coloring problem, in which one needs to color directed paths on a symmetric directed graph with a minimum number of colors, in such a way that paths using the same arc of the graph have different colors. This classic combinatorial problem finds applications in the minimization of the number of wavelengths in wavelength division multiplexin...

We give a bijection between partially directed paths in the symmetric wedge y = ±x and matchings, which sends north steps to nestings. This gives a bijective proof of a result of Prellberg et al. that was first discovered through the corresponding generating functions: the number of partially directed paths starting at the origin confined to the symmetric wedge y = ±x with k north steps is equa...

The Gallai-Milgram theorem says that the vertex set of any digraph with stability number k can be partitioned into k directed paths. In 1990, Hahn and Jackson conjectured that this theorem is best possible in the following strong sense. For each positive integer k, there is a digraph D with stability number k such that deleting the vertices of any k− 1 directed paths in D leaves a digraph with ...

Plumage coloration in birds plays a critical role in communication and can be under selection throughout the annual cycle as a sexual and social signal. However, for migratory birds, little is known about the acquisition and maintenance of colorful plumage during the nonbreeding period. Winter habitat could influence the quality of colorful plumage, ultimately carrying over to influence sexual ...

To contribute to young children's development, sensory enrichment is often provided via colorful play areas. However, little is known about the effects of colorful environments on children while they engage in age-appropriate tasks and games. Studies in adults suggest that aspects of color can distract attention and impair performance, and children are known to have less developed attentional a...

Motivated by Asynchronous Transfer Mode (ATM) in telecommunication networks, we investigate the problem of designing a directed virtual topology on a directed physical topology, which consists in nding a set of directed virtual paths (VPs) satisfying some constraints in terms of load (the number of VPs sharing a physical link) and hop count (the number of VPs used to establish a connection). Fo...

The concept of a line digraph is generalized to that of a directed path graph. The directed path graph → Pk(D) of a digraph D is obtained by representing the directed paths on k vertices of D by vertices. Two vertices are joined by an arc whenever the corresponding directed paths in D form a directed path on k + 1 vertices or form a directed cycle on k vertices in D. In this introductory paper ...

The well known types of routes in graphs and directed graphs, such as walks, trails, paths, and induced paths, are characterized using axioms on vertex sequences. Thus non-graphic characterizations of the various types of routes are obtained.