Given a graph G = (V, E) and two vertices s, t ∈ V , s 6= t , the Menger problem is to find a maximum number of disjoint paths connecting s and t . Depending on whether the input graph is directed or not, and what kind of disjointness criterion is demanded, this general formulation is specialized to the directed or undirected vertex, and the edge or arc disjoint Menger problem, respectively. Fo...

We construct, using mild combinatorial hypotheses, a real Menger set that is not Scheepers, and two sets are in all finite powers, with non-Menger product. By forcing-theoretic argument, we show the same holds Blass–Shelah

A fast random walk (FRW) algorithm is adapted to compute diffusion-weighted NMR signals in a Menger sponge which is formed by multiple channels of broadly distributed sizes and often considered as a model for soils and porous materials. The self-similar structure of a Menger sponge allows for rapid simulations that were not feasible by other numerical techniques. The role of multiple length sca...

A construction based on the Biggs-Smith graph is shown to produce an edge-disjoint union of 102 copies of K4 forming a {K4, L(Q3)}K3 -ultrahomogeneous graph dressed as the non-line-graphical Menger graph of a self-dual (1024)-configuration. This stands in contrast to the selfdual (424)-configuration of [8], whose Menger graph is a non-line-graphical {K4, K2,2,2}K2 -ultrahomogeneous graph.

and Applied Analysis 3 Clearly, every Menger PN-space is probabilistic metric space having a metrizable uniformity on X if supa<1T a, a 1. Definition 1.3. Let X,Λ, T be a Menger PN-space. i A sequence {xn} in X is said to be convergent to x in X if, for every > 0 and λ > 0, there exists positive integer N such that Λxn−x > 1 − λ whenever n ≥ N. ii A sequence {xn} in X is called Cauchy sequence ...