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$$(k,j)$$-coloring of sparse graphs. (English) Zbl 1239.05059
Summary: A graph $$G$$ is called ($$k,j$$)-colorable, if the vertex set of $$G$$ can be partitioned into subsets $$V_{1}$$ and $$V_{2}$$ such that the graph $$G[V_{1}]$$ induced by the vertices of $$V_{1}$$ has maximum degree at most $$k$$ and the graph $$G[V_{2}]$$ induced by the vertices of $$V_{2}$$ has maximum degree at most $$j$$. In this paper, we give a sufficient condition of ($$k,j$$)-colorability for graphs with bounded maximum average degree.

##### MSC:
 05C15 Coloring of graphs and hypergraphs 05C42 Density (toughness, etc.) 90C05 Linear programming 05C35 Extremal problems in graph theory 05C07 Vertex degrees
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