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Exixtence of vertices of local connectivityk in digraphs of large outdegree

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Abstract

For every positive integerk, there is a positive integerf(k) such that every finite digraph of minimum outdegreef(k) contains verticesx, y joined byk openly disjoint paths.

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References

  1. A. Frank, T. Ibaraki, andH. Nagamochi: On sparse subgraphs preserving connectivity properties,J. Graph Theory,17 (1993), 275–281.

    Google Scholar 

  2. Y. O. Hamidoune: Sur les atomes d'un graphe orienté,C. R. Acad. Sci. Paris Sér. A,284 (1977), 1253–1256.

    Google Scholar 

  3. Y. O. Hamidoune: Quelques problèmes de connexité dans les graphes orientés,J. Combin. Theory B,30 (1981), 1–10.

    Google Scholar 

  4. W. Mader: Homomorphieeigenschaften und mittlere Kantendichte von Graphen,Math. Ann.,174 (1967), 265–268.

    Google Scholar 

  5. W. Mader: Existenz gewisser Konfigurationen inn-gesättigten Graphen und in Graphen genügend großer Kantendichte,Math. Ann.,194 (1971), 295–312.

    Google Scholar 

  6. W. Mader: Grad und lokaler Zusammenhang in endlichen Graphen,Math. Ann.,205 (1973), 9–11.

    Google Scholar 

  7. W. Mader: Ecken mit starken Zusammenhangseigenschaften in endlichen Graphen,Math. Ann.,216 (1975), 123–126.

    Google Scholar 

  8. W. Mader: Degree and local connectivity in digraphs,Combinatorica,5 (1985), 161–165.

    Google Scholar 

  9. W. Mader: Ecken von kleinem Grad in kritischn-fach zusammenhängenden Digraphen.J. Combin. Theory B,53 (1991), 260–272.

    Google Scholar 

  10. H. Sachs: Einführung in die Theorie der endlichen Graphen,Carl Hanser Verlag, München 1971.

    Google Scholar 

  11. C. Thomassen: Even cycles in directed graphs,European J. of Combinatorics,6 (1985), 85–89.

    Google Scholar 

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Mader, W. Exixtence of vertices of local connectivityk in digraphs of large outdegree. Combinatorica 15, 533–539 (1995). https://doi.org/10.1007/BF01192525

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  • DOI: https://doi.org/10.1007/BF01192525

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