For every 2-polymatroid, the chromatic polynomial counting its matroid decompositions equals a rational multiple of the chromatic polynomial of some graph, and special hypergraphs realize the graph coloring number as the minimal decomposition size.
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Decomposable polymatroids and connections with graph coloring
For every 2-polymatroid, the chromatic polynomial counting its matroid decompositions equals a rational multiple of the chromatic polynomial of some graph, and special hypergraphs realize the graph coloring number as the minimal decomposition size.