The Lovász-Cherkassky theorem in countable graphs

Lovász and Cherkassky discovered in the 1970s independently that if G is a finite graph with given set T of terminal vertices such inner Eulerian respect to T, then maximal number edge-disjoint paths connecting distinct ∑t∈Tλ(t,T−t) where λ local edge-connectivity function. The optimality system T-paths Lovász-Cherkassky theorem witnessed by existence certain cuts Menger's theorem. infinite generalisation Aharoni Berger (earlier known as Erdős-Menger Conjecture) together characterization graphs due Nash-Williams makes it possible generalise for structural way. aim this paper formulate prove countable graphs.