On the hamiltonicity of line graphs of locally finite, 6-edge-connected graphs
Journal of Graph Theory
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A well-known conjecture of Erdõs states that given aninfinite graph G and sets A, ⊆V(G), there exists a family of disjoint A -B paths 𝓅 together with an A - Bseparator X consisting of a choice of one vertex from eachpath in 𝓅. There is a natural extension of this conjecturein which A, B, and X may contain ends as wellas vertices. We prove this extension by reducing it to the vertexversion, which was recently proved by Aharoni and Berger. ©2005 Wiley Periodicals, Inc. J Graph Theory 50: 199211, 2005