Nonrepetitive colorings of graphs of bounded tree-width

A sequence of the form s1s2 . . . sms1s2 . . . sm is called a repetition. A vertex-coloring of a graph is called nonrepetitive if none of its paths is repetitively colored. We answer a question of Grytczuk [5] by proving that every outerplanar graph has a nonrepetitive 12-coloring. We also show that graphs of tree-width t have nonrepetitive 4t-colorings.

• Type: Journal
• Year: 2008
• Where: DM
• Authors: André Kündgen, Michael J. Pelsmajer
• Keywords: DM 2008, Form S1s2, Outerplanar Graph, Show