Stronger bounds for generalized degrees and Menger path systems
For positive integers d and m, let 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 conditions that ensure that is satisfied have been investigated. In particular, it has been shown, for fixed positive...