The Lovász-Cherkassky theorem in infinite graphs

The study of infinite analogues of classical results in finite combinatorics goes back to Erdős and his influential Erdős–Menger conjecture, now known as the Aharoni–Berger theorem. This result extends Menger’s theorem from finite to infinite graphs showing that its essential structural content persists in the infinite setting. Lovász and Cherkassky independently established a minimax theorem on packing edge-disjoint paths with endpoints in a prescribed set T of vertices, assuming that all remaining vertices have even degree. We provide an infinite, structural generalization of their theorem. Our emphasis in this talk is on the set-theoretic parts of the proof.