Ramsey theory for graph connectivity

  title={Ramsey theory for graph connectivity},
  author={David W. Matula},
  journal={Journal of Graph Theory},
r,(k) Denotes the smallest integer ouch that any c-edge-coloring of the r#) vertex complete graph has a monochromatic k-connected subgraph. For any c, k 1 2 , we show 2 4 k 1) t 1 I rJk) < c(k1)+ 1, and further that 4(k1) + 1 I rdk) < (3 t fi) ( k 1) + 1. Some exact values for various Ramsey Connectivity numbers are also computed. I . INTRODUCTION AND SUMMARY We consider a variation of the origlinal problem of Ramsey [8]. Specifically, in the graph theoretic interpretation of Ramsey’s problem… CONTINUE READING

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