Sciweavers

FOCS
2002
IEEE

A Lower Bound for Testing 3-Colorability in Bounded-Degree Graphs

13 years 8 months ago
A Lower Bound for Testing 3-Colorability in Bounded-Degree Graphs
We consider the problem of testing 3-colorability in the bounded-degree model. We show that, for small enough ε, every tester for 3colorability must have query complexity Ω(n). This is the first linear lower bound for testing a natural graph property in the bounded-degree model. An Ω( √ n) lower bound was previously known. For one-sided error testers, we also show an Ω(n) lower bound for testers that distinguish 3-colorable graphs from graphs that are (1/3 − α)-far from 3-colorable, for arbitrarily small α. In contrast, a polynomial time algorithm by Frieze and Jerrum distinguishes 3-colorable graphs from graphs that are 1/5-far from 3-colorable. As a by-product of our techniques, we obtain tight unconditional lower bounds on the approximation ratios achievable by sublinear time algorithms for Max E3SAT, Max E3LIN-2 and other problems.
Andrej Bogdanov, Kenji Obata, Luca Trevisan
Added 14 Jul 2010
Updated 14 Jul 2010
Type Conference
Year 2002
Where FOCS
Authors Andrej Bogdanov, Kenji Obata, Luca Trevisan
Comments (0)