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End-Devouring Rays

Author(s): Georgakopoulos

\begin{problem} Let $G$ be a graph, $\omega$ a countable end of $G$, and $K$ an infinite set of pairwise disjoint $\omega$-rays in $G$. Prove that there is a set $K'$ of pairwise disjoint $\omega$-rays that devours $\omega$ such that the set of starting vertices of rays in $K'$ equals the set of starting vertices of rays in $K$. \end{problem}

Keywords: end; ray

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