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Abstract: Let H be a fixed directed graph on h vertices, let G be a directed graph on n vertices and suppose that at least #n edges have to be deleted from it to make it H-free. We show that in this case G contains at least f(#, H)n copies of H. This is proved by establishing a directed version of Szemeredi's regularity lemma, and implies that for every H there is a one-sided error property tester whose query complexity is bounded by a function of # only for testing the property PH of being... (Update)
Context of citations to this paper: More
...#n edges contains at least #(# ) copies of K t,t . In fact, sampling 1 # O(t) vertices su#ces, by a special case of a 8 result in [5] improving the estimate in [1] It is also worth noting that there are simple graph properties (like the property of containing at least n 4...
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BibTeX entry: (Update)
N. Alon and A. Shapira, Testing subgraphs in directed graphs, Proc. of the 35 ACM STOC, ACM Press (2003), to appear. http://citeseer.ist.psu.edu/alon03testing.html More
@misc{ alon03testing,
author = "N. Alon and A. Shapira",
title = "Testing subgraphs in directed graphs",
text = "N. Alon and A. Shapira, Testing subgraphs in directed graphs, Proc. of
the 35 ACM STOC, ACM Press (2003), to appear.",
year = "2003",
url = "citeseer.ist.psu.edu/alon03testing.html" }
Citations (may not include all citations):167 Property testing and its connection to learning and approxim.. - Goldreich, Goldwasser et al.
115 Robust characterization of polynomials with applications to .. - Rubinfeld, Sudan - 1996
51 Quick approximation to matrices and applications - Frieze, Kannan - 1999
50 The algorithmic aspects of the Regularity Lemma - Alon, Duke et al.
33 Regular languages are testable with a constant number of que.. - Alon, Krivelevich et al.
24 Property testing - Ron - 2001
18 Testing of clustering - Alon, Dar et al. - 2000
16 On graphs with small subgraphs of large chromatic number (context) - Rodl, Duke - 1985
15 Regular partitions of graphs (context) - Szemeredi - 1978
14 The art of uninformed decisions: A primer to property testin.. - Fischer - 2001
14 Three theorems regarding testing graph properties - Goldreich, Trevisan - 2001
14 Springer-Verlag (context) - Diestel, Theory et al. - 2000
14 Property testing in computational geometry (context) - Czumaj, Sohler - 2000
14 towards a unified measure of complexity (context) - Yao, computation - 1977
13 Testing subgraphs in large graphs (context) - Alon - 2001
13 Szemeredi's regularity lemma and its applications in graph t.. (context) - Komlos, Simonovits - 1996
12 On sets of integers which contain no three terms in arithmet.. (context) - Behrend - 1946
12 Lower bounds of tower type for Szemeredi's Uniformity Lemma (context) - Gowers - 1997
11 Extremal graphs without large forbidden subgraphs (context) - Bollobas, Erdos et al. - 1978
10 A Lower Bound for Testing 3-Colorability in Boundeddegree Gr.. - Bogdanov, Obata et al. - 2002
10 Discrete Math (context) - Hell, Nesetril et al. - 1992
9 Supersaturated graphs and hypergraphs (context) - Erdos, Simonovits - 1983
7 Discrete Math (context) - Alon, Krivelevich et al. - 2002
6 Testing hypergraph coloring - Czumaj, Sohler - 2001
4 Duality of graph homomorphisms (context) - Hell, Nesetril et al. - 1996
4 On extremal problems of graphs and generalized graphs (context) - Erdos - 1964
3 Random Sampling and Approximation of MAX-CSP Problems - Alon, Vega et al. - 2002
2 Turan numbers of bipartite graphs and related Ramseytype que.. (context) - Alon, Krivelevich et al.
2 on Foundations of Computer Science (context) - Alon, Fischer et al.
2 Annual ACM-SIAM SODA (context) - Alon, Shapira et al. - 2002
1 ect of two cycles on the complexity of colorings by directed.. (context) - Bang-Jensen, Hell - 1990
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