Subgraphs Satisfying MSO Properties on z-Topologically Orderable Digraphs

  title={Subgraphs Satisfying MSO Properties on z-Topologically Orderable Digraphs},
  author={Mateus de Oliveira Oliveira},
We introduce the notion of z-topological orderings for digraphs. We prove that given a digraph G on n vertices admitting a z-topological order- ing, together with such an ordering, one may count the number of subgraphs of G that at the same time satisfy a monadic second order formula {\phi} and are the union of k directed paths, in time f ({\phi}, k, z) * n^O(k*z) . Our result implies the polynomial time solvability of many natural counting problems on digraphs admitting z-topological orderings… 
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