Partitions of graphs with high minimum degree or connectivity

  title={Partitions of graphs with high minimum degree or connectivity},
  author={Daniela K{\"u}hn and Deryk Osthus},
  journal={J. Comb. Theory, Ser. B},
We prove that there exists a function f ðcÞ such that the vertex set of every f ðcÞ-connected graph G can be partitioned into sets S and T such that each vertex in S has at least c neighbours in T and both G1⁄2S and G1⁄2T are c-connected. This implies that there exists a function gðc;HÞ such that every gðc;HÞ-connected graph contains a subdivision TH of H so that G VðTHÞ is c-connected. We also prove an analogue with connectivity replaced by minimum degree. Furthermore, we show that there… CONTINUE READING

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