Suppose that (s1, t1), ..., (sk, tk) are pairs of vertices of a graph. When can one choose a path between si and ti for each i, all pairwise edge-disjoint? Menger's theorem answers this when s1, ..., sk, t1, ..., tk take only two distinct values, but the general problem is unsolved. We settle the two next simplest cases,. (i) when k = 2, and. (ii) when s1, ..., sk, t1, ..., tk take only three distinct values-the solution to this is obtained by applying a theorem of Mader. We obtain both good characterizations and good algorithms for these problems. The analogous "vertex-disjoint" problems are also solved.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics