Partition of graphs with condition on the connectivity and minimum degree

Abstract

C. Thomassen and M. Szegedy proved the existence of a functionf(s, t) such that the points of anyf(s, t)-connected graph have a decomposition into two non-empty sets such that the subgraphs induced by them ares-connected andt-connected, respectively. We prove, thatf(s, t) ≦ 4s+4t − 13 and examine a similar problem for the minimum degree.

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References

  1. [1]

    C. Thomassen, Graph decomposition with constraints on the connectivity and minimum degree,J. Graph Theory, to appear.

  2. [2]

    W. Mader, Existenzn-fach zusammenhängender Teilgraphen in Graphen genügend grossen Kantendichte,Abh. Math. Sem. Hamburg Univ. 37 (1972), 86–97.

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    M. Szegedy, unpublished.

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Hajnal, P. Partition of graphs with condition on the connectivity and minimum degree. Combinatorica 3, 95–99 (1983). https://doi.org/10.1007/BF02579344

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AMS subject classification (1980)

  • 05 C 40