Generalized degrees and Menger path systems

Generalized Degrees and Menger Path Systems

Faudree, R.J., R.J. Gould and L.M. Lesniak, Generalized degrees and Menger path systems, Discrete Applied Mathematics 37/38 (1992) 179-191. For positive integers d and W, let P&,,(G) denote the property that between each pair of vertices of the graph G, there are m internally disjoint paths of length at most d. For a positive integer t, a graph G satisfies the minimum generalized degree conditi...

Stronger bounds for generalized degress and Menger path systems

For positive integers d and m, let Pd,m(G) denote the property that between each pair of vertices of the graph G , there are m internally vertex disjoint paths of length at most d. For a positive integer t a graph G satisfies the minimum generalized degree condition δt(G) ≥ s if the cardinality of the union of the neighborhoods of each set of t vertices of G is at least s. Generalized degree co...

Generalized Distance and Common Fixed Point Theorems in Menger Probablistic Metric Spaces

Degrees of difficulty of generalized

Important examples of Π 1 classes of functions f ∈ ω are the classes of sets (elements of 2) which separate a given pair of disjoint r.e. sets: S2(A0, A1) := { f ∈ 2 : (∀i < 2)(∀x ∈ Ai)f(x) 6= i }. A wider class consists of the classes of functions f ∈ k which in a generalized sense separate a k-tuple of r.e. sets (not necessarily pairwise disjoint) for each k ∈ ω: Sk(A0, . . . , Ak−1) := { f ∈...

Bihomogeneity and Menger Manifolds

It is shown that for every triple of integers (α, β, γ) such that α ≥ 1, β ≥ 1, and γ ≥ 2, there is a homogeneous, non-bihomogeneous continuum whose every point has a neighborhood homeomorphic the Cartesian product of Menger compacta μ ×μ × μ . In particular, there is a homogeneous, non-bihomogeneous, Peano continuum of covering dimension four.