Large Monochromatic Triple Stars in Edge Colourings

  title={Large Monochromatic Triple Stars in Edge Colourings},
  author={Shoham Letzter},
  journal={Journal of Graph Theory},
  • Shoham Letzter
  • Published 17 October 2013
  • Mathematics
  • Journal of Graph Theory
Following problems posed by Gyárfás 2011, we show that for every r‐edge‐colouring of Kn there is a monochromatic triple star of order at least n/(r−1) , improving Ruszinkó's result 2012. An edge colouring of a graph is called a local r‐colouring if every vertex spans edges of at most r distinct colours. We prove the existence of a monochromatic triple star with at least rn/(r2−r+1) vertices in every local r‐colouring of Kn . 
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I would like to thank Trinity College and Department of Pure Mathematics and Mathematical Statistics for their generous financial support and hospitality during PhD studies.
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