A separator theorem for graphs of bounded genus
Journal of Algorithms
A separator theorem for graphs with an excluded minor and its applications
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Testing the diameter of graphs
Random Structures & Algorithms
Testing properties of directed graphs: acyclicity and connectivity
Random Structures & Algorithms
A Lower Bound for Testing 3-Colorability in Bounded-Degree Graphs
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Property testing in massive graphs
Handbook of massive data sets
Algorithms column: sublinear time algorithms
ACM SIGACT News
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Tight Bounds for Testing Bipartiteness in General Graphs
SIAM Journal on Computing
Abstract Combinatorial Programs and Efficient Property Testers
SIAM Journal on Computing
Every monotone graph property is testable
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
A Characterization of the (natural) Graph Properties Testable with One-Sided Error
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Testing triangle-freeness in general graphs
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A combinatorial characterization of the testable graph properties: it's all about regularity
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Graph limits and parameter testing
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Every minor-closed property of sparse graphs is testable
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
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We study graph properties which are testable for bounded degree graphs in time independent of the input size. Our goal is to distinguish between graphs having a predetermined graph property and graphs that are far from every graph having that property. It is believed that almost all, even very simple graph properties require a large complexity to be tested for arbitrary (bounded degree) graphs. Therefore in this paper we focus our attention on testing graph properties for special classes of graphs. We call a graph family non-expanding if every graph in this family is not a weak expander (its expansion is O(1/log2 n), where n is the graph size). A graph family is hereditary if it is closed under vertex removal. Similarly, a graph property is hereditary if it is closed under vertex removal. Next, we call a graph property Π to be testable for a graph family F if for every graph G ε F, in time independent of the size of G we can distinguish between the case when G satisfies property Π and when it is far from every graph satisfying property Π. In this paper we prove that In the bounded degree graph model, any hereditary property is testable if the input graph belongs to a hereditary and non-expanding family of graphs. As an application, our result implies that, for example, any hereditary property (e.g., k-colorability, H-freeness, etc.) is testable in the bounded degree graph model for planar graphs, graphs with bounded genus, interval graphs, etc. No such results have been known before and prior to our work, in the bounded degree graph model very few graph properties have been known to be testable for any graph classes.