consider the random walk among n places with n(n - 1)/2 transports. we attach an exponential random variable xij to each transport between places pi and pj and take these random variables mutually independent. if transports are possible or impossible independently with probability p and 1-p, respectively, then we give a lower bound for the distribution function of the smallest path at point log...

Two new path problems in graphs are studied: MINRANGE, i.e., find a path from a vertex s to a vertex 1 with the smallest possible range of arc lengths. and MINRATIO, i.e., find such a path for which the ratio of the largest to the smallest arc length is minimum. Several bicriterion extensions of these problems are also considered. Ke_vwords: Bicriterion paths; Range; Ratio

The classical PERT approach uses the path with the largest expected duration as the critical path to estimate the probability of completing a network by a given deadline. However, in general, such a path is not the most critical path (MCP) and does not have the smallest estimate for the probability of completion time. The main idea of this paper is derived from the domination structure between ...

We examine whether the Phelps–Koopmans theorem is valid in models with nonconvex production technologies. We argue that a nonstationary path that converges to a capital stock above the smallest golden rule may indeed be efficient. This finding has the important implication that “capital overaccumulation” need not always imply inefficiency. Under mild regularity and smoothness assumptions, we pr...

Consider the random walk among N places with N(N - 1)/2 transports. We attach an exponential random variable Xij to each transport between places Pi and Pj and take these random variables mutually independent. If transports are possible or impossible independently with probability p and 1-p, respectively, then we give a lower bound for the distribution function of the smallest path at point log...

A set of vertices $S$ in a connected graph $G$ is a different-distance set if, for any vertex $w$ outside $S$, no two vertices in $S$ have the same distance to $w$.The lower and upper different-distance number of a graph are the order of a smallest, respectively largest, maximal different-distance set.We prove that a different-distance set induces either a special type of path or an independent...

A path separator of a graph G is a set of paths P = {P1, . . . , Pt} such that for every pair of edges e, f ∈ E(G), there exist paths Pe, Pf ∈ P such that e ∈ E(Pe), f 6∈ E(Pe), e 6∈ E(Pf ) and f ∈ E(Pf ). The path separation number of G, denoted psn(G), is the smallest number of paths in a path separator. We shall estimate the path separation number of several graph families, including complet...