Degree and local connectivity in digraphs

Abstract

It is shown that there is a digraphD of minimum outdegree 12m and\(\mathop {\max }\limits_{x \ne y} \) μ(x, y; D)=11m, but every digraphD of minimum outdegreen contains verticesxy withλ(x, y; D)≧n−1, whereμ(x, y; D) andλ(x, y; D) denote the maximum number of openly disjoint and edge-disjoint paths, respectively.

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Mader, W. Degree and local connectivity in digraphs. Combinatorica 5, 161–165 (1985). https://doi.org/10.1007/BF02579379

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AMS subject classification (1980)

  • 05 C 40
  • 05 C 20
  • 05 C 38