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Parameterized (Modular) Counting and Cayley Graph Expanders
2021
We study the problem #EdgeSub(Φ) of counting k-edge subgraphs satisfying a given graph property Φ in a large host graph G. Building upon the breakthrough result of Curticapean, Dell and Marx (STOC 17), we express the number of such subgraphs as a finite linear combination of graph homomorphism counts and derive the complexity of computing this number by studying its coefficients. Our approach relies on novel constructions of low-degree Cayley graph expanders of p-groups, which might be of
doi:10.4230/lipics.mfcs.2021.84
fatcat:xwizn2lowjb3tb77e7gpfmh3si