Nonrepetitive colorings of trees

@article{Bresar2007NonrepetitiveCO,
  title={Nonrepetitive colorings of trees},
  author={Bostjan Bresar and Jaroslaw Grytczuk and Sandi Klavzar and Staszek Niwczyk and Iztok Peterin},
  journal={Discrete Mathematics},
  year={2007},
  volume={307},
  pages={163-172}
}
A coloring of the vertices of a graph G is nonrepetitive if no path in G forms a sequence consisting of two identical blocks. The minimum number of colors needed is the Thue chromatic number, denoted by π(G). A famous theorem of Thue asserts that π(P ) = 3 for any path P with at least 4 vertices. In this paper we study the Thue chromatic number of trees. In view of the fact that π(T ) is bounded by 4 in this class we aim to describe the 4-chromatic trees. In particular, we study the 4-critical… CONTINUE READING
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