Edge disjoint paths in hypercubes and folded hypercubes with conditional faults

It is known that edge disjoint paths is closely related to the edge connectivity and the multicommodity flow problems. In this paper, we study the edge disjoint paths in hypercubes and folded hypercubes with edge faults. We first introduce the F-strongly Menger edge connectivity of a graph, and we show that in all n  -dimensional hypercubes (folded hypercubes, respectively) with at most 2n−4(2n−2,2n−4(2n−2, respectively) edges removed, if each vertex has at least two fault-free adjacent vertices, then every pair of vertices u and v are connected by min{deg(u), deg(v)} edge disjoint paths, where deg(u) and deg(v) are the remaining degree of vertices u and v, respectively.