Advertisement

Combinatorica

, Volume 28, Issue 3, pp 357–372 | Cite as

Cycle lengths in sparse graphs

  • Benny SudakovEmail author
  • Jacques Verstraëte
Article

Mathematics Subject Classification (2000)

05C35 05C38 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    N. Alon, M. Krivelevich and B. Sudakov: Turán numbers of bipartite graphs and related Ramsey-type questions, Combinatorics, Probability and Computing 12 (2003), 477–494.zbMATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    N. Alon, L. Rónyai and T. Szabó: Norm-graphs: variations and applications, J. Combinatorial Theory Ser. B 76 (1999), 280–290.zbMATHCrossRefGoogle Scholar
  3. [3]
    B. Bollobás: Cycles modulo k, Bull. London Math. Soc. 9 (1977), 97–98.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    B. Bollobás and A. Thomason: Weakly pancyclic graphs, J. Combinatorial Theory Ser. B 77 (1999), 121–137.zbMATHCrossRefGoogle Scholar
  5. [5]
    A. Bondy: Pancyclic graphs I, J. Combinatorial Theory Ser. B 11 (1971), 80–84.zbMATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    A. Bondy and M. Simonovits: Cycles of even length in graphs, J. Combinatorial Theory Ser. B 16 (1974), 97–105.zbMATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    M. N. Ellingham and D. K. Menser: Girth, minimum degree, and circumference; J. Graph Theory 34(3) (2000), 221–233.zbMATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    P. Erdős: Some of my favourite problems in various branches of combinatorics, Matematiche (Catania) 47 (1992), 231–240.MathSciNetGoogle Scholar
  9. [9]
    P. Erdős: Some of my favorite solved and unsolved problems in graph theory, Quaestiones Math. 16 (1993), 333–350.MathSciNetGoogle Scholar
  10. [10]
    P. Erdős: Some old and new problems in various branches of combinatorics, in: Graphs and combinatorics, (Marseille, 1995); also: Discrete Mathematics 165–166(15) (1997), 227–231.Google Scholar
  11. [11]
    P. Erdős, R. Faudree, C. Rousseau and R. Schelp: The number of cycle lengths in graphs of given minimum degree and girth, Discrete Mathematics 200 (1999), 55–60.CrossRefMathSciNetGoogle Scholar
  12. [12]
    G. Fan: Distribution of cycle lengths in graphs, J. Combinatorial Theory Ser. B 84 (2002), 187–202.zbMATHCrossRefGoogle Scholar
  13. [13]
    R. Gould, P. Haxell and A. Scott: A note on cycle lengths in graphs, Graphs and Combinatorics 18 (2002), 491–498.zbMATHCrossRefMathSciNetGoogle Scholar
  14. [14]
    A. Gyárfás: Graphs with κ odd cycle lengths, Discrete Mathematics 103 (1992), 41–48.zbMATHCrossRefMathSciNetGoogle Scholar
  15. [15]
    A. Gyárfás, J. Komlós and E. Szemerédi: On the distribution of cycle lengths in graphs, J. Graph Theory 8 (1984), 441–462.zbMATHCrossRefMathSciNetGoogle Scholar
  16. [16]
    J. Kollár, L. Rónyai and T. Szabó: Norm-graphs and bipartite Turán numbers, Combinatorica 16(3) (1996), 399–406.zbMATHCrossRefMathSciNetGoogle Scholar
  17. [17]
    T. Kővári, V. T. Sós and P. Turán: On a problem of K. Zarankiewicz, Colloquium Math. 3 (1954), 50–57.MathSciNetGoogle Scholar
  18. [18]
    L. Lovász: Combinatorial Problems and Exercises, 2nd Ed., North-Holland, Amsterdam, 1993.zbMATHGoogle Scholar
  19. [19]
    A. Lubotzky, R. Phillips and P. Sarnak: Ramanujan Graphs, Combinatorica 8(3) (1988), 261–277.zbMATHCrossRefMathSciNetGoogle Scholar
  20. [20]
    G. Margulis: Explicit group-theoretic constructions of combinatorial schemes and their applications in the construction of expanders and concentrators, Problems Inform. Transmission 24 (1988), 39–46.zbMATHMathSciNetGoogle Scholar
  21. [21]
    O. Ore: On a graph theorem by Dirac, J. Combinatorial Theory 2 (1967), 383–392.zbMATHCrossRefMathSciNetGoogle Scholar
  22. [22]
    L. Pósa: Hamiltonian circuits in random graphs, Discrete Mathematics 14 (1976), 359–364.zbMATHCrossRefMathSciNetGoogle Scholar
  23. [23]
    J. Verstraëte: On arithmetic progressions of cycle lengths in graphs, Combinatorics Probability and Computing 9 (2000), 369–373.zbMATHCrossRefMathSciNetGoogle Scholar
  24. [24]
    C. Q. Zhang: Circumference and girth, J. Graph Theory 13(4) (1989), 485–490.CrossRefMathSciNetGoogle Scholar
  25. [25]
    B. Z. Zhao: The circumference and girth of a simple graph (Chinese), J. Northeast Univ. Tech. 13(3) (1992), 294–296.MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California, Los AngelesLos AngelesUSA
  2. 2.Department of MathematicsUniversity of California, San DiegoLa JollaUSA

Personalised recommendations