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Corpus ID: 119306037

Birthday Paradox, Monochromatic Subgraphs, and the Second Moment Phenomenon

@article{Bhattacharya2017BirthdayPM,
title={Birthday Paradox, Monochromatic Subgraphs, and the Second Moment Phenomenon},
author={B. Bhattacharya and S. Mukherjee},
journal={arXiv: Probability},
year={2017}
}

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

L. Beineke & R. Wilson (Eds.), Topics in Chromatic Graph Theory, Encyclopedia of Mathematics and its Applications, Cambridge University Press, 327– 357