A note about online nonrepetitive coloring $k$-trees

TL;DR

This paper proves that online nonrepetitive coloring of graphs with bounded tree-width can be achieved with a finite number of colors, generalizing offline results to online settings for various graph classes.

Contribution

It establishes the first online nonrepetitive coloring bounds for k-trees, extending offline results to an online context with explicit color bounds.

Findings

Online nonrepetitive coloring of k-trees with 4^k colors.

Coloring of cycles, trees, and series-parallel graphs with 16 colors.

Generalization of offline nonrepetitive coloring results to online algorithms.

Abstract

We prove that it is always possible to color online nonrepetitively any (partial) $k$-tree (that is, graphs with tree-width at most $k$) with $4^k$ colors. This implies that it is always possible to color online nonrepetitively cycles, trees and series-parallel graphs with $16$ colors. Our results generalize the respective (offline) nonrepetitive coloring results.