Menger's theorem is extended to ends of digraphs, equating the maximum number of disjoint paths between ends to the minimum separator size, and applied to characterize the combined degree of ends.
Polat,A mengerian theorem for infinite graphs with ideal points, Journal of Combinatorial Theory, Series B51(1991), no
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Menger's theorem for ends of digraphs
Menger's theorem is extended to ends of digraphs, equating the maximum number of disjoint paths between ends to the minimum separator size, and applied to characterize the combined degree of ends.