Consider modeling the problem as a flow network where each edge has a capacity of 1, then apply the max-flow min-cut theorem to find the solution.

Explore how the Ford-Fulkerson method can be adapted to count edge-disjoint paths by iteratively finding augmenting paths and reducing residual capacities.

Investigate the relationship between edge-disjoint paths and the concept of *blocking flows* in Dinic's algorithm, and how it can be used to optimize the solution.