Résumé
Let
k
be a nonnegative integer, and let
m
k
=
4
(
k
+
1
)
(
k
+
3
)
k
2
+
6
k
+
6
. We prove that every simple graph with maximum average degree less than
m
k
decomposes into a forest and a subgraph with maximum degree at most
k
(furthermore, when
k
≤
3
both subgraphs can be required to be forests). It follows that every simple graph with maximum average degree less than
m
k
has game coloring number at most
4
+
k
.