Constructing one-to-many disjoint paths in folded hypercubes

Routing functions have been shown effective in deriving disjoint paths in the hypercube. In this paper, using a minimal routing function, k+1 disjoint paths from one node to another k+1 distinct nodes are constructed in a kdimensional folded hypercube whose maximal length is not greater than the diameter plus one, which is minimum in the worst case. For the general case, the maximal length is nearly optimal (⩽ the maximal distance between the two end nodes of these k+1 paths plus two). As a by-product, the Rabin number of the folded hypercube is obtained, which is an open problem raised by S.C. Liaw and G.J. Chang (1999)