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- W2950193710 abstract "We consider the question of the existence of homomorphisms between $G_{n,p}$ and odd cycles when $p=c/n,,1<cleq 4$. We show that for any positive integer $ell$, there exists $epsilon=epsilon(ell)$ such that if $c=1+epsilon$ then w.h.p. $G_{n,p}$ has a homomorphism from $G_{n,p}$ to $C_{2ell+1}$ so long as its odd-girth is at least $2ell+1$. On the other hand, we show that if $c=4$ then w.h.p. there is no homomorphism from $G_{n,p}$ to $C_5$. Note that in our range of interest, $chi(G_{n,p})=3$ w.h.p., implying that there is a homomorphism from $G_{n,p}$ to $C_3$." @default.
- W2950193710 created "2019-06-27" @default.
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- W2950193710 date "2014-04-19" @default.
- W2950193710 modified "2023-09-23" @default.
- W2950193710 title "Between 2- and 3-colorability" @default.
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