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- W4386857841 abstract "We say that a sequence a1 . . . a2t of integers is repetitive if ai = ai+t for every i ϵ {1,...,t}. A walk in a graph G is a sequence v1 . . . vr of vertices of G in which vivi+1 ϵ E(G) for every i ϵ {1,..., r - 1}. Given a k-coloring c: V(G) → {1,..., k} of V(G), we say that c is walk-nonrepetitive if for every t ϵ N, for every walk v1 . . . v2t in G the sequence c(V1) . . . c(v2t) is not repetitive unless vi = vi+t for every i ϵ {1,..., t}, and the walk-nonrepetitive chromatic number σ(G) of G is the minimum k for which G has a walk-nonrepetitive k-coloring. Let Cn denote the cycle with n vertices. In this paper we show that σ(Cn) = 4 whenever n ≥ 4 and n ∉ {5,7}, which answers a question posed by Barát and Wood in 2008." @default.
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- W4386857841 date "2023-01-01" @default.
- W4386857841 modified "2023-09-27" @default.
- W4386857841 title "On nonrepetitive colorings of cycles" @default.
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- W4386857841 doi "https://doi.org/10.1016/j.procs.2023.08.241" @default.
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