Comparing the strength of query types in property testing: The case of testing k-colorability

Ido Ben-Eliezer*, Tali Kaufman, Michael Krivelevich, Dana Ron

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We study the power of four query models in the context of property testing in general graphs (i.e., with arbitrary edge densities), where our main case study is the problem of testing k-colorability. Two query types, which have been studied extensively in the past, are pair queries and neighbor queries. The former corresponds to asking whether there is an edge between any particular pair of vertices, and the latter to asking for the i'th neighbor of a particular vertex. We show that while for pair queries, testing k-colorability requires a number of queries that is a monotone decreasing function in the average degree d, the query complexity in the case of neighbor queries remains roughly the same for every density and for large values of k. We also consider a combined model that allows both types of queries, and we propose a new, stronger, query model, related to the field of Group Testing. We give one-sided error upper and lower bounds for all the models, where the bounds are nearly tight for three of the models. In some of the cases our lower bounds extend to two-sided error algorithms. The problem of testing k-colorability was previously studied in the contexts of dense and sparse graphs, and in our proofs we unify approaches from those cases, and also provide some new tools and techniques that may be of independent interest.

Original languageEnglish
Title of host publicationProperty Testing - Current Research and Surveys
Number of pages7
StatePublished - 2010
EventMini-Workshop on Property Testing - Beijing, China
Duration: 8 Jan 201010 Jan 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6390 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


ConferenceMini-Workshop on Property Testing


  • group queries
  • k-colorability
  • neighbor queries
  • pair queries


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