MSOL partitioning problems on graphs of bounded treewidth and clique-width

We show that a class of vertex partitioning problems that can be expressed in monadic second order logic (MSOL) are polynomials on graphs of bounded clique-width. This class includes coloring, H-free coloring, domatic number and partition into perfect graphs. Moreover we show that a class of vertex and edge partitioning problems are polynomials on graphs of bounded treewidth.

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