Every minor-closed property of sparse graphs is testable

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2008, Pages 39-44

  Benjamini, Itai ^a   Schramm, Oded ^a   Shapira, Asaf ^a  

^a MICROSOFT RESEARCH   (United States)

Author keywords

Graph algorithms; Minor closed properties; Property testing

Indexed keywords

COMPUTATIONAL GEOMETRY; TREES (MATHEMATICS);

BOUNDED DEGREE GRAPHS; BOUNDED DEGREES; CONVERGENT SEQUENCES; DENSE GRAPHS; FOLLOWING PROBLEMS; GRAPH ALGORITHMS; GRAPH G; GRAPH PROPERTIES; MINOR CLOSED PROPERTIES; OF GRAPHS; PROPERTY TESTING; SHARP CONTRASTS; SPARSE GRAPHS;

GRAPH THEORY;

EID: 57049177156     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (42)

1. N. Alon, E. Fischer, I, Newman and A. Shapira, A combinatorial characterization of the testable graph properties: it's all about regularity, Proc. of STOC'06, 251-260. Also, SIAM J. on Computing, to appear.
2. N. Alon, P. D. Seymour and R. Thomas, A separator theorem for non-planar graphs, J. Amer. Math. Soc. 3 (1990), 801-808.
3. N. Alon and A. Shapira, A characterization of the (natural) graph properties testable with one-sided error, Proc. of FOCS 2005, 429-438. Also, SIAM J. on Computing, to appear.
4. N. Alon and A. Shapira, Homomorphisms in graph property testing, in Topics in discrete mathematics, 281-313, Springer, Berlin, 2006.
5. N. Alon and A. Shapira, A separation theorem in property testing, Combinatorica, to appear.
6. M. Blum, M. Luby and R. Rubinfeld, Self-testing/correcting with applications to numerical problems, JCSS 47 (1993), 549-595.
7. H. L. Bodlaender, Discovering treewidth, Lecture Notes in Computer Science, 3381 (2005), 1-16.
8. A. Bogdanov, K. Obata, and L. Trevisan, A lower bound for testing 3-colorability in bounded-degree graphs, FOCS 2002, 93-102.
9. C. Borgs, J. Chayes, L. Lovász, V. T. Sos, B. Szegedy, and K. Vesztergombi, Graph limits and parameter-testing, STOC 2006, 261-270.
10. A. Czumaj, A. Shapira, and C. Sohler, Testing hereditary properties of non-expanding bounded-degree graphs, submitted (full version of [13]).
11. A. Czumaj and C. Sohler, Testing expansion in bounded-degree graphs, Proc. of FOCS 2007, 570-578.
12. A. Czumaj and C. Sohler, Sublinear-time algorithms, Bulletin of the EATCS, 89 (2006) 23-47.
13. A. Czumaj and C. Sohler, On testable properties in bounded degree graphs, Proc. of SODA 2007, 494-501.
14. E. Demaine, M. Hajiaghayi and K. Kawarabayashi, Algorithmic graph minor theory: decomposition, approximation, and coloring, Proc. of FOCS 2005, 637-646.
15. R. Diestel, Graph Theory (Third Edition), Springer, Heidenberg, 2005.
16. C. Domingo and J. Shawe-Taylor, The Complexity of Learning Minor-Closed Graph Classes, Proc. of Algorithmic Learning Theory 1995, 249-260.
17. R. Downey and M. Fellows, Parameterized Complexity, Springer, 1999.
18. G. Elek, The combinatorial cost, to appear in L'Enseignement Mathématique
19. G. Elek, A Regularity lemma for bounded degree graphs and its applications: parameter testing and infinite volume limits, arXiv:07112800, 2007.
20. E. Fischer, The art of uninformed decisions: A primer to property testing, The Computational Complexity Column of The Bulletin of the European Association for Theoretical Computer Science 75 (2001), 97-126.
21. O. Goldreich, S. Goldwasser and D. Ron, Property testing and its connection to learning and approximation, J. of the ACM 45(4): 653-750 (1998).
22. O. Goldreich and D. Ron, Property Testing in Bounded-Degree Graphs, Algorithmica 32 (2002), 302-343.
23. O. Goldreich and D. Ron, A sublinear bipartiteness tester for bounded degree graphs, Combinatorica, 19 (1999), 335-373.
24. O. Goldreich and L. Trevisan, Three theorems regarding testing graph properties, Random Structures and Algorithms, 23(1):23-57, 2003.
25. J. E. Hopcroft and R. E. Tarjan, Efficient planarity testing, J. of the ACM, 21 (1974), 549-568.
26. A. Kostochka, The minimum Hadwiger number for graphs with a given mean degree of vertices, Metody Diskret. Analliz. 38 (1982), 37-58 [in Russion].
27. A. Kostochka, A lower bound for the Hadwiger number of graphs by their average degree, Combinatorica, 4 (1984), 307-316.
28. K. Kuratowski, Sur le problème des courbes gauches en topologie, Fund. Math. 15: 271-283.
29. R. J. Lipton and R. E. Tarjan, A separator theorem for planar graphs, SIAM J. Appl. Math., 36 (1979), 177-189.
30. R. J. Lipton and R. E. Tarjan, Applications of a planar separator theorem, S1AM J. on Computing 9 (1980), 615-627.
31. L. Lovász, Graph minor theory, Bull. Amer. Math. Soc. 43 (2006), no. 1, 75-86.
32. M. Parnas and D. Ron, Testing the diameter of graphs, Random structures and algorithms, 20 (2002), 165-183.
33. N. Robertson and P.D. Seymour: Graph minors XIII. The disjoint paths problem, J. Combin. Theory Ser. B 63 (1995), 65-110.
34. N. Robertson and P. D. Seymour, Graph minors. XX. Wagner's Conjecture, J. Combin. Theory Ser. B 92 (2004), 325-357.
35. R. Rubinfeld, Sublinear time algorithms, in International Congress of Mathematicians. Vol. III, 1095-1110, Eur. Math. Soc., Zürich, 2006.
36. D. Ron, Property testing, in: P. M. Pardalos, S. Rajasekaran, J. Reif and J. D. P. Rolim, editors, Handbook of Randomized Computing, Vol. II, Kluwer Academic Publishers, 2001, 597-649.
37. R. Rubinfeld and M. Sudan, Robust characterization of polynomials with applications to program testing, SIAM J. on Computing, 25 (1996), 252-271.
38. O. Schramm, Graph sequences with hyperfinite limits are hyperfinite, arXiv:0711.3808, 2007.
39. E. Szemerédi, Regular partitions of graphs, In: Proc. Collogue Inter. CNRS (J. C. Bermond, J. C. Fournier, M. Las Vergnas and D. Sotteau, eds.), 1978, 399-401.
40. A. Thomason, An extremal function for contractions of graphs, Math. Proc. Cambridge Philos. Soc. 95 (1984), 261-265.
41. A. Thomason, The extremal function for complete minors, J. of Combinatorial Theory Series B, 81 (2001), 318-338.
42. K. Wagner, Über eine eigenschaft der ebenen komplexe, Math. Ann. 114 (1937), 570-590.