T-joins in infinite graphs as edge-disjoint system of paths matching the vertices in $T$

Abstract

We characterize the class of infinite connected graphs $G$ for which there exists a $T$-join for any choice of an infinite $T\subseteq V(G)$. We also show that the following well-known fact remains true in the infinite case. If $G$ is connected and does not contain a $T$-join, then it will if we either remove an arbitrary vertex from $T$ or add any new vertex to $T$.