Czumaj, Artur, Shapira, Asaf and Sohler, Christian. (2009) Testing hereditary properties of nonexpanding bounded-degree graphs. SIAM Journal on Computing, Vol.38 (No.6). pp. 2499-2510. ISSN 00975397

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Abstract

We study graph properties that 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 well known that in the bounded-degree graph model (where two graphs are considered “far” if they differ in $\varepsilon n$ edges for a positive constant $\varepsilon$), many graph properties cannot be tested even with a constant or even with a polylogarithmic number of queries. Therefore in this paper we focus our attention on testing graph properties for special classes of graphs. Specifically, we show that every hereditary graph property is testable with a constant number of queries provided that every sufficiently large induced subgraph of the input graph has poor expansion. This 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, very few graph properties have been known to be testable with a constant number of queries for general graph classes in the bounded-degree graph model.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Divisions:	Faculty of Science > Computer Science
Library of Congress Subject Headings (LCSH):	Graph theory, Graph algorithms, Algorithms
Journal or Publication Title:	SIAM Journal on Computing
Publisher:	Society for Industrial and Applied Mathematics
ISSN:	00975397
Date:	April 2009
Volume:	Vol.38
Number:	No.6
Page Range:	pp. 2499-2510
Identification Number:	10.1137/070681831
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	National Science Foundation (U.S.) (NSF), Deutsche Forschungsgemeinschaft (DFG), Engineering and Physical Sciences Research Council (EPSRC)
Grant number:	CCR-0313219 (NSF), EP/D063191/1 (EPSRC), 0354600 (NSF), Me 872/8-3 (DFG)
Version or Related Resource:	A preliminary version of this paper, entitled “On testable properties in bounded degree graphs,” authored by the first and third authors, appeared in the Proceedings of the 18th Annual Symposium on Discrete Algorithms (SODA), New Orleans, LA, 2007, pp. 494–501.
URI:	http://wrap.warwick.ac.uk/id/eprint/37021

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