Corpus ID: 119306037

Birthday Paradox, Monochromatic Subgraphs, and the Second Moment Phenomenon

  title={Birthday Paradox, Monochromatic Subgraphs, and the Second Moment Phenomenon},
  author={B. Bhattacharya and S. Mukherjee},
  journal={arXiv: Probability},
  • B. Bhattacharya, S. Mukherjee, S. Mukherjee
  • Published 2017
  • Mathematics
  • arXiv: Probability
  • What is the chance that among a group of $n$ friends, there are $s$ friends all of whom have the same birthday? This is the celebrated birthday problem which can be formulated as the existence of a monochromatic $s$-clique $K_s$ ($s$-matching birthdays) in the complete graph $K_n$, where every vertex of $K_n$ is uniformly colored with $365$ colors (corresponding to birthdays). More generally, for a general connected graph $H$, let $T(H, G_n)$ be the number of monochromatic copies of $H$ in a… CONTINUE READING
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