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- W1981002960 abstract "A nonrepetitive coloring of a path is a coloring of its vertices such that the sequence of colors along the path does not contain two identical, consecutive blocks. The remarkable construction of Thue asserts that three colors are enough to color nonrepetitively paths of any length. A nonrepetitive coloring of a graph is a coloring of its vertices such that all simple paths are nonrepetitively colored. Assume that each vertex $v$ of a graph $G$ has assigned a set (list) of colors $L_v$. A coloring is chosen from ${{L_v}_{vin V(G)}}$ if the color of each $v$ belongs to $L_v$. The Thue choice number of $G$, denoted by $pi_l(G)$, is the minimum $k$ such that for any list assignment ${{L_v}}$ of $G$ with each $|{L_v}|geqslant k$ there is a nonrepetitive coloring of $G$ chosen from ${{L_v}}$. Alon et al. proved in 2002 that $pi_l(G)=O(Delta^2)$ for every graph $G$ with maximum degree at most $Delta$. We propose an almost linear bound in $Delta$ for trees, namely, for any $varepsilon>0$ there is a..." @default.
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- W1981002960 modified "2023-09-25" @default.
- W1981002960 title "Nonrepetitive Choice Number of Trees" @default.
- W1981002960 doi "https://doi.org/10.1137/120866361" @default.
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