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- W4297923215 abstract "Let $T(K_{1, r}, G_n)$ be the number of monochromatic copies of the $r$-star $K_{1, r}$ in a uniformly random coloring of the vertices of the graph $G_n$. In this paper we provide a complete characterization of the limiting distribution of $T(K_{1, r}, G_n)$, in the regime where $mathbb E(T(K_{1, r}, G_n))$ is bounded, for any growing sequence of graphs $G_n$. The asymptotic distribution is a sum of mutually independent components, each term of which is a polynomial of a single Poisson random variable of degree at most $r$. Conversely, any limiting distribution of $T(K_{1, r}, G_n)$ has a representation of this form. Examples and connections to the birthday problem are discussed." @default.
- W4297923215 created "2022-10-01" @default.
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- W4297923215 date "2017-04-15" @default.
- W4297923215 modified "2023-09-27" @default.
- W4297923215 title "Limit Theorems for Monochromatic Stars" @default.
- W4297923215 doi "https://doi.org/10.48550/arxiv.1704.04674" @default.
- W4297923215 hasPublicationYear "2017" @default.
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