Every monotone graph property is testable

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 es 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 . 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 Szemer?edi'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...

• Type: Conference
• Year: 2005
• Where: STOC
• Authors: Noga Alon, Asaf Shapira
• Keywords: Algorithms, Monotone Graph Properties, Monotone Graph Property, STOC 2005, Testable Graph Properties