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SIAMDM
2008

Testing Triangle-Freeness in General Graphs

10 years 4 months ago
Testing Triangle-Freeness in General Graphs
In this paper we consider the problem of testing whether a graph is triangle-free, and more generally, whether it is H-free, for a fixed subgraph H. The algorithm should accept graphs that are triangle-free and reject graphs that are far from being triangle-free in the sense that a constant fraction of the edges should be removed in order to obtain a triangle-free graph. The algorithm is allowed a small probability of error. This problem has been studied quite extensively in the past, but the focus was on dense graphs, that is, when d = (n), where d is the average degree in the graph and n is the number of vertices. Here we study the complexity of the problem in general graphs, that is, for varying d. In this model a testing algorithm is allowed to ask neighbor queries (i.e., "what is the i-th neighbor of vertex v"), vertex-pair queries (i.e., "is there an edge between vertices v and u"), and degree queries (i.e., "what is the degree of vertex v"). Our ma...
Noga Alon, Tali Kaufman, Michael Krivelevich, Dana
Added 14 Dec 2010
Updated 14 Dec 2010
Type Journal
Year 2008
Where SIAMDM
Authors Noga Alon, Tali Kaufman, Michael Krivelevich, Dana Ron
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