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# Thue choosability of trees

Abstract : A vertex colouring of a graph G is nonrepetitive if for any path $P = (v_1, v_2,\dots., v_{2r})$ in $G$, the first half is coloured differently from the second half. The Thue choice number of $G$ is the least integer $l$ such that for every $l$-list assignment $L$ of $G$, there exists a nonrepetitive $L$-colouring of $G$. We prove that for any positive integer $l$, there is a tree $T$ with $\pi_{ch}(T) > l$. On the other hand, it is proved that if $G'$ is a graph of maximum degree $\Delta$, and $G$ is obtained from $G'$ by attaching to each vertex $v$ of $G'$ a graph of tree-depth at most $d$ rooted at $v$, then $\pi_{ch}(G)\leq c(\Dela, d)$ for some constant $c(\Delta, d)$ depending only on $\Delta$ and $d$.
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https://hal.archives-ouvertes.fr/hal-00656797
Contributor : Patrice Ossona de Mendez <>
Submitted on : Thursday, January 5, 2012 - 10:46:16 AM
Last modification on : Wednesday, November 4, 2020 - 6:08:03 PM

### Citation

Francesca Fiorenzi, Pascal Ochem, Patrice Ossona de Mendez, Xuding Zhu. Thue choosability of trees. Discrete Applied Mathematics, Elsevier, 2011, 159, pp.2045-2049. ⟨10.1016/j.dam.2011.07.017⟩. ⟨hal-00656797⟩

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