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Counting Restricted Homomorphisms via Möbius Inversion over Matroid Lattices
[article]
2017
arXiv
pre-print
We present a framework for the complexity classification of parameterized counting problems that can be formulated as the summation over the numbers of homomorphisms from small pattern graphs H_1,...,H_l to a big host graph G with the restriction that the coefficients correspond to evaluations of the M\"obius function over the lattice of a graphic matroid. This generalizes the idea of Curticapean, Dell and Marx [STOC 17] who used a result of Lov\'asz stating that the number of subgraph
arXiv:1706.08414v1
fatcat:54q2ljvnp5ewboak3d67ij73oq