Embeddings of graphs of fixed treewidth and bounded degree

Let  F  be any family of graphs of fixed treewidth and bounded degree. We construct a quadratic-time algorithm for calculating the genus distribution of the graphs in F . Within a post-order traversal of the decomposition tree, the algorithm involves a full-powered upgrading of production rules and root-popping . This algorithm for calculating genus distributions in quadratic time complements an algorithm of Kawarabayashi, Mohar, and Reed for calculating the minimum genus of a graph of bounded treewidth in linear time.

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