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Erschienen in:
2007 | OriginalPaper | Buchkapitel
Nonrepetitive Graph Coloring
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A coloring of the vertices of a graph
G
is
nonrepetitive
if no simple path in
G
looks like
a
1
a
2
...
a
n
a
1
a
2
...
a
n
. The minimum number of colors needed for a graph
G
is denoted by π(
G
). For instance, by the famous 1906 theorem of Thue, π(
G
) = 3 if
G
is a simple path with at least 4 vertices. This implies that π(
G
) ≤ 4 if Δ(
G
) ≤ 2. But how large can π(
G
) be for cubic graphs,
κ
-trees, or planar graphs? This paper is a small survey of problems and results of the above type.