Testing subgraphs in large graphs

N. Alon

doi:10.1109/sfcs.2001.959918

Testing subgraphs in large graphs

N. Alon

Research output: Contribution to journal › Conference article › peer-review

28 Scopus citations

Abstract

Let H be a fixed graph with h vertices, let G be a graph on n vertices and suppose that at least εn² edges have to be deleted from it to make it H-free. It is known that in this case G contains at least f(ε, H)n^h copies of H. We show that the largest possible function f(ε, H) is polynomial in ε if and only if H is bipartite. This implies that there is a one-sided error property tester for checking H-freeness, whose query complexity is polynomial in 1/ε, if and only if H is bipartite.

Original language	English
Pages (from-to)	434-441
Number of pages	8
Journal	Annual Symposium on Foundations of Computer Science - Proceedings
DOIs	https://doi.org/10.1109/sfcs.2001.959918
State	Published - 1 Jan 2001
Externally published	Yes
Event	42nd Annual Symposium on Foundations of Computer Science - Las Vegas, NV, United States Duration: 14 Oct 2001 → 17 Oct 2001

ASJC Scopus subject areas

Hardware and Architecture

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10.1109/sfcs.2001.959918

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title = "Testing subgraphs in large graphs",

abstract = "Let H be a fixed graph with h vertices, let G be a graph on n vertices and suppose that at least εn2 edges have to be deleted from it to make it H-free. It is known that in this case G contains at least f(ε, H)nh copies of H. We show that the largest possible function f(ε, H) is polynomial in ε if and only if H is bipartite. This implies that there is a one-sided error property tester for checking H-freeness, whose query complexity is polynomial in 1/ε, if and only if H is bipartite.",

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N2 - Let H be a fixed graph with h vertices, let G be a graph on n vertices and suppose that at least εn2 edges have to be deleted from it to make it H-free. It is known that in this case G contains at least f(ε, H)nh copies of H. We show that the largest possible function f(ε, H) is polynomial in ε if and only if H is bipartite. This implies that there is a one-sided error property tester for checking H-freeness, whose query complexity is polynomial in 1/ε, if and only if H is bipartite.

AB - Let H be a fixed graph with h vertices, let G be a graph on n vertices and suppose that at least εn2 edges have to be deleted from it to make it H-free. It is known that in this case G contains at least f(ε, H)nh copies of H. We show that the largest possible function f(ε, H) is polynomial in ε if and only if H is bipartite. This implies that there is a one-sided error property tester for checking H-freeness, whose query complexity is polynomial in 1/ε, if and only if H is bipartite.

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M3 - Conference article

AN - SCOPUS:0035179610

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JF - Annual Symposium on Foundations of Computer Science - Proceedings

T2 - 42nd Annual Symposium on Foundations of Computer Science

Y2 - 14 October 2001 through 17 October 2001

ER -

Testing subgraphs in large graphs

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