Removal Lemma for Infinitely-many Forbidden Hypergraphs and Property Testing
نویسنده
چکیده
We prove a removal lemma for infinitely-many forbidden hypergraphs. It affirmatively settles a question on property testing raised by Alon and Shapira (2005) [2, 3]. All monotone hypergraph properties and all hereditary partite hypergraph properties are testable. Our proof constructs a constant-time probabilistic algorithm to edit a small number of edges. It also gives a quantitative bound in terms of a coloring number of the property. It is based on a new hypergraph regularity lemma [14].
منابع مشابه
Regular partitions of hypergraphs and property testing
About 30 years ago Szemerédi developed the regularity method for graphs, which was a key ingredient in the proof of his famous density result concerning the upper density of subsets of the integers which contain no arithmetic progression of fixed length. Roughly speaking, the regularity lemma asserts, that the vertex set of every graph can be partitioned into a constant number of classes such t...
متن کاملA VARIATIONAL APPROACH TO THE EXISTENCE OF INFINITELY MANY SOLUTIONS FOR DIFFERENCE EQUATIONS
The existence of infinitely many solutions for an anisotropic discrete non-linear problem with variable exponent according to p(k)–Laplacian operator with Dirichlet boundary value condition, under appropriate behaviors of the non-linear term, is investigated. The technical approach is based on a local minimum theorem for differentiable functionals due to Ricceri. We point out a theorem as a spe...
متن کاملA Polynomial Regularity Lemma for Semialgebraic Hypergraphs and Its Applications in Geometry and Property Testing
Fox, Gromov, Lafforgue, Naor, and Pach proved a regularity lemma for semi-algebraic kuniform hypergraphs of bounded complexity, showing that for each ǫ > 0 the vertex set can be equitably partitioned into a bounded number of parts (in terms of ǫ and the complexity) so that all but an ǫ-fraction of the k-tuples of parts are homogeneous. We prove that the number of parts can be taken to be polyno...
متن کاملA characterization of testable hypergraph properties [Extended Abstract]
We provide a combinatorial characterization of all testable properties of k-graphs (i.e. k-uniform hypergraphs). Here, a k-graph property P is testable if there is a randomized algorithm which makes a bounded number of edge queries and distinguishes with probability 2/3 between k-graphs that satisfy P and those that are far from satisfying P. For the 2graph case, such a combinatorial characteri...
متن کاملModel Theory and Hypergraph Regularity
1. Ultrafilters, ultraproducts and ultralimits 1 1.1. Filters and ultrafilters 1 1.2. Ultralimits 2 1.3. Some model-theoretic notation 3 1.4. Ultraproducts of first-order structures 3 1.5. References 6 2. Graph regularity and measures on ultraproducts 6 2.1. Szemerédi’s regularity lemma 6 2.2. Finitely additive measures 7 2.3. Obtaining countable additivity 9 2.4. Integration for charges (signe...
متن کامل