Edge-disjoint double rays in infinite graphs: a Halin type result

TL;DR

This paper proves a conjecture by Andreae that any infinite graph containing a finite number of edge-disjoint double rays actually contains infinitely many such double rays, extending understanding of infinite graph structures.

Contribution

It establishes that the presence of a finite number of edge-disjoint double rays implies infinitely many, confirming a long-standing conjecture in infinite graph theory.

Findings

Any graph with k edge-disjoint double rays has infinitely many such rays.

Confirms Andreae's 1981 conjecture about infinite graphs.

Extends the theory of edge-disjoint structures in infinite graphs.

Abstract

We show that any graph that contains k edge-disjoint double rays for any k>0 contains also infinitely many edge-disjoint double rays. This was conjectured by Andreae in 1981.