# Complexity of Counting Subgraphs: Only the Boundedness of the Vertex-Cover Number Counts

@article{Curticapean2014ComplexityOC, title={Complexity of Counting Subgraphs: Only the Boundedness of the Vertex-Cover Number Counts}, author={Radu Curticapean and D. Marx}, journal={2014 IEEE 55th Annual Symposium on Foundations of Computer Science}, year={2014}, pages={130-139} }

For a class C of graphs, #Sub(C) is the counting problem that, given a graph H from C and an arbitrary graph G, asks for the number of subgraphs of G isomorphic to H. It is known that if C has bounded vertex-cover number (equivalently, the size of the maximum matching in C is bounded), then #Sub(C) is polynomial-time solvable. We complement this result with a corresponding lower bound: if C is any recursively enumerable class of graphs with unbounded vertexcover number, then #Sub(C) is #W[1… CONTINUE READING

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