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We establish a result on edge‐disjoint paths with prescribed ends in infinite trees and apply this to prove the conjecture of Eggleton and Skilton [1] that any connected graph has a decomposition into chains such that at most one of these is one‐way infinite and each vertex is the end‐vertex of at most one of the chains and no vertex of infinite degree is such an end‐vertex. We also give a necessary and sufficient condition for a graph to have a decomposition into one‐way infinite chains.
Bulletin of the London Mathematical Society – Wiley
Published: May 1, 1986
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