Paired $(n-1)$-to-$(n-1)$ disjoint path covers in bipartite transposition-like graphs

A paired k-to-k disjoint path cover of a graph G is a collection of pairwise disjoint path subgraphs P₁,P₂,,Pₖ such that each Pᵢ has prescribed vertices sᵢ and tᵢ as endpoints and the union of P₁,P₂,,Pₖ contains all vertices of G. In this paper, we introduce bipartite transposition-like graphs, which are inductively constructed from lower ranked bipartite transposition-like graphs. We show that every rank n bipartite transposition-like graph G admit a paired $(n-1)$-to-$(n-1)$ disjoint path cover for all choices of S=₁,s₂,,sₙ₋₁\ and T=₁,t₂,,tₙ₋₁\, provided that S is in one partite set of G and T is in the other.