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- W2617470265 abstract "Let $Omega_q$ denote the set of proper $q$-colorings of the random graph $G_{n,m}, m=dn/2$ and let $H_q$ be the graph with vertex set $Omega_q$ and an edge ${sigma,tau}$ where $sigma,tau$ are mappings $[n]to[q]$ iff $h(sigma,tau)=1$. Here $h(sigma,tau)$ is the Hamming distance $|{vin [n]:sigma(v)neqtau(v)}|$. We show that w.h.p. $H_q$ contains a single giant component containing almost all colorings in $Omega_q$ if $d$ is sufficiently large and $qgeq frac{cd}{log d}$ for a constant $c>3/2$." @default.
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- W2617470265 date "2017-05-22" @default.
- W2617470265 modified "2023-09-23" @default.
- W2617470265 title "Constraining the clustering transition for colorings of sparse random graphs" @default.
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