NDLI: Every monotone graph property is testable

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Every monotone graph property is testable

Content Provider	ACM Digital Library
Author	Alon, Noga Shapira, Asaf
Abstract	A graph property is called monotone if it is closed under taking (not necessarily induced) subgraphs (or, equivalently, if it is closed under removal of edges and vertices). Many monotone graph properties are some of the most well-studied properties in graph theory, and the abstract family of all monotone graph properties was also extensively studied. Our main result in this paper is that any monotone graph property can be tested with one-sided error, and with query complexity depending only on ε. This result unifies several previous results in the area of property testing, and also implies the testability of well-studied graph properties that were previously not known to be testable. At the heart of the proof is an application of a variant of Szemerédi's Regularity Lemma. The main ideas behind this application may be useful in characterizing all testable graph properties, and in generally studying graph property testing.As a byproduct of our techniques we also obtain additional results in graph theory and property testing, which are of independent interest. One of these results is that the query complexity of testing testable graph properties with one-sided error may be arbitrarily large. Another result, which significantly extends previous results in extremal graph-theory, is that for any monotone graph property P, any graph that is ε -far from satisfying P, contains a subgraph of size depending on ε only, which does not satisfy P. Finally, we prove the following compactness statement: If a graph G is ε-far from satisfying a (possibly infinite) set of graph properties P, then it is at least δ P ε-far from satisfying one of the properties.
Starting Page	128
Ending Page	137
Page Count	10
File Format	PDF
ISBN	1581139608
DOI	10.1145/1060590.1060611
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2005-05-22
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Monotone properties Regularity lemma Property testing
Content Type	Text
Resource Type	Article

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