Advertisement

Efficient Removal Without Efficient Regularity

  • Lior GishbolinerEmail author
  • Asaf Shapira
Article

Mathematics Subject Classification (2010)

05C35 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    N. Alon: Testing subgraphs in large graphs, Random Structures and Algorithms 21 (2002), 359–370.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    N. Alon, E. Fischer, M. Krivelevich and M. Szegedy: Efficient testing of large graphs, Combinatorica 20 (2000), 451–476.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    N. Alon, E. Fischer, and I. Newman: Testing of bipartite graph properties, SIAM Journal on Computing 37 (2007), 959–976.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    N. Alon and J. Fox: Easily testable graph properties, Combin. Probab. Comput. 24 (2015), 646–657.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    N. Alon and A. Shapira: A characterization of easily testable induced subgraphs, Combin. Probab.Comput. 15 (2006), 791–805.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    N. Alon and A. Shapira: A characterization of the (natural) graph properties testable with one-sided error, SIAM Journal on Computing 37 (2008), 1703–1727.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    N. Alon and J. H. Spencer: The Probabilistic Method, 3rd ed., Wiley, 2008.CrossRefzbMATHGoogle Scholar
  8. [8]
    L. Avigad and O. Goldreich: Testing graph blow-up, Proc. of APPROX-RANDOM 2011, 389–399.zbMATHGoogle Scholar
  9. [9]
    D. Conlon and J. Fox: Bounds for graph regularity and removal lemmas, GAFA 22 (2012), 1191–1256.MathSciNetzbMATHGoogle Scholar
  10. [10]
    D. Conlon and J. Fox: Graph removal lemmas, Surveys in Combinatorics, Cambridge university press, 2013, 1–50.zbMATHGoogle Scholar
  11. [11]
    P. Erdős: On extremal problems of graphs and generalized graphs, Israel J. Math. 2 (1964), 183–190.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    P. Erdős: On some problems in graph theory, combinatorial analysis and combinatorial number theory, in: Graph theory and combinatorics (Cambridge, 1983), 1–17. Academic Press, London, 1984.Google Scholar
  13. [13]
    J. Fox: A new proof of the graph removal lemma, Ann. of Math. 174 (2011), 561–579.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    L. Gishboliner and A. Shapira: Removal lemmas with polynomial bounds, Proc. of STOC 2017.CrossRefzbMATHGoogle Scholar
  15. [15]
    O. Goldreich: Introduction to Property Testing, Forthcoming book, 2017.CrossRefzbMATHGoogle Scholar
  16. [16]
    O. Goldreich, S. Goldwasser and D. Ron: Property testing and its connection to learning and approximation, J. ACM 45 (1998), 653–750.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    O. Goldreich and D. Ron: On proximity-oblivious testing, SIAM J. on Computing 40 (2011), 534–566.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    T. Gowers: Lower bounds of tower type for Szemerédi’s uniformity lemma, Geom. Funct. Anal. 7 (1997), 322–337.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    A. Gyárfás, A. Hubenko and J. Solymosi: Large cliques in C4-free graphs, Combinatorica 22 (2002), 269–274.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    L. Lovász: Large networks and graph limits (Vol. 60), Providence: American Mathematical Society (2012).CrossRefzbMATHGoogle Scholar
  21. [21]
    G. Moshkovitz and A. Shapira: A sparse regular aproximation lemma, Transactions of the AMS, to appear.Google Scholar
  22. [22]
    H. Prömel and A. Steger: Excluding induced subgraphs: quadrilaterals, Random Structures and Algorithms 2 (1991), 55–71.MathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    V. Rödl and R. Duke: On graphs with small subgraphs of large chromatic number, Graphs and Combinatorics 1 (1985), 91–96.MathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    V. Rödl and M. Schacht: Regularity lemmas for graphs, Fete of Combinatorics and Computer Science, Bolyai Soc. Math. Stud. 20 (2010), 287–325.MathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    I. Z. Ruzsa and E. Szemerédi: Triple systems with no six points carrying three triangles, in: Combinatorics (Keszthely, 1976), Coll. Math. Soc. J. Bolyai 18, Volume II, 939–945.Google Scholar
  26. [26]
    E. Szemerédi: Regular partitions of graphs, in: Proc. Colloque Inter. CNRS, 1978, 399–401.Google Scholar

Copyright information

© János Bolyai Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesTel Aviv UniversityTel AvivIsrael

Personalised recommendations