Counting induced k-vertex subgraphs with automorphism group exactly Q is #W[1]-hard for every finite group Q, via clique-scaffold reductions from k-clique.
Large networks and graph limits, volume 60 of American Mathematical Society Colloquium Publications
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Flag algebras yield sharp inducibility bounds for 36 six-vertex graphs with stability proofs in 32 cases and conjectures for 12 more.
Sufficient conditions are given for pseudo-likelihood estimation of both parameters in the Potts model at rate sqrt(N) for bounded-degree or irregular graphs, with impossibility shown for certain dense regular graphs, plus a new concentration inequality via nonlinear large deviations.
Random cographs on n vertices converge in probability to a graphon limit.
A functional central limit theorem for pattern frequencies in 2D samples enables nonparametric goodness-of-fit, two-sample, and symmetry tests for copulas, with bootstrap critical values and parametric examples.
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Counting Small Induced Subgraphs: Hardness of Symmetry-Based Properties
Counting induced k-vertex subgraphs with automorphism group exactly Q is #W[1]-hard for every finite group Q, via clique-scaffold reductions from k-clique.
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The inducibility of 6-vertex graphs
Flag algebras yield sharp inducibility bounds for 36 six-vertex graphs with stability proofs in 32 cases and conjectures for 12 more.
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Joint Estimation in Potts Model
Sufficient conditions are given for pseudo-likelihood estimation of both parameters in the Potts model at rate sqrt(N) for bounded-degree or irregular graphs, with impossibility shown for certain dense regular graphs, plus a new concentration inequality via nonlinear large deviations.
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Graphon convergence of random cographs
Random cographs on n vertices converge in probability to a graphon limit.
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Pattern-based tests for two-dimensional copulas
A functional central limit theorem for pattern frequencies in 2D samples enables nonparametric goodness-of-fit, two-sample, and symmetry tests for copulas, with bootstrap critical values and parametric examples.