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- W2892008004 abstract "Let $C_{n}$ be a cycle of length $n$. As an application of Szemeredi's regularity lemma, Łuczak ($R(C_n,C_n,C_n)leq (4+o(1))n$, J. Combin. Theory Ser. B, 75 (1999), 174--187) in fact established that $K_{(8+o(1))n}to(C_{2n+1},C_{2n+1},C_{2n+1})$. In this paper, we strengthen several results involving cycles. Let $mathcal{G}(n,p)$ be the random graph. We prove that for fixed $0 0$, there exists an integer $n_0$ such that for all integer $n_3>n_0$, we have a.a.s. that begin{align*} mathcal{G}((8+delta)n_1,p) to (C_{2n_1+1},C_{2n_2+1},C_{2n_3+1}). end{align*} Moreover, we prove that for fixed $0 0$ with same order, i.e. $n_2=Theta(n_1)$ and $n_3=Theta(n_1)$, we have a.a.s. that begin{align*} mathcal{G}(2n_1+n_2+n_3+o(1)n_1,p) to (C_{2n_1},C_{2n_2},C_{2n_3}). end{align*} Similar results for the two color case are also obtained." @default.
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- W2892008004 date "2018-09-04" @default.
- W2892008004 modified "2023-09-27" @default.
- W2892008004 title "Cycle Ramsey numbers for random graphs" @default.
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