Advertisement

Graphs, Part II: More Advanced Notions

Chapter
Part of the Universitext book series (UTX)

Abstract

In this section, we take a closer look at the structure of cycles in a finite graph G. It turns out that there is a dual notion to that of a cycle, the notion of a cocycle.

Keywords

Bipartite Graph Planar Graph Hamiltonian Cycle Incidence Matrix Maximum Match 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Claude Berge. Graphs and Hypergraphs. Amsterdam: Elsevier North-Holland, first edition, 1973.MATHGoogle Scholar
  2. 2.
    Marcel Berger. Géométrie 1. Nathan, 1990. English edition: Geometry 1, Universitext, New York: Springer Verlag.Google Scholar
  3. 3.
    Norman Biggs. Algebraic Graph Theory, volume 67 of Cambridge Tracts in Mathematics. Cambridge, UK: Cambridge University Press, first edition, 1974.MATHGoogle Scholar
  4. 4.
    Béla Bollobas. Modern Graph Theory. GTM No. 184. New York: Springer Verlag, first edition, 1998.MATHGoogle Scholar
  5. 5.
    J. Cameron, Peter. Combinatorics: Topics, Techniques, Algorithms. Cambridge, UK: Cambridge University Press, first edition, 1994.MATHGoogle Scholar
  6. 6.
    Fan R. K. Chung. Spectral Graph Theory, vol. 92 of Regional Conference Series in Mathematics. Providence, RI: AMS, first edition, 1997.Google Scholar
  7. 7.
    H. Cormen, Thomas, E. Leiserson, Charles, L. Rivest, Ronald, and Clifford Stein. Introduction to Algorithms. Cambridge, MA: MIT Press, second edition, 2001.MATHGoogle Scholar
  8. 8.
    Peter Cromwell. Polyhedra. Cambridge, UK: Cambridge University Press, first edition, 1994.Google Scholar
  9. 9.
    Reinhard Diestel. Graph Theory. GTM No. 173. New York: Springer Verlag, third edition, 2005.Google Scholar
  10. 10.
    Jean Gallier. What’s so Special about Kruskal’s Theorem and the Ordinal Γ0? Annals of Pure and Applied Logic, 53:199–260, 1991.MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Jean H. Gallier. Geometric Methods and Applications, for Computer Science and Engineering. TAM, Vol. 38. New York: Springer, first edition, 2000.Google Scholar
  12. 12.
    Chris Godsil and Gordon Royle. Algebraic Graph Theory. GTM No. 207. New York: Springer Verlag, first edition, 2001.Google Scholar
  13. 13.
    Jonathan L. Gross, and Thomas W. Tucker. Topological Graph Theory. New York: Dover, first edition, 2001.MATHGoogle Scholar
  14. 14.
    Victor Guillemin and Alan Pollack. Differential Topology. Englewood Cliffs, NJ: Prentice Hall, first edition, 1974.MATHGoogle Scholar
  15. 15.
    Frank Harary. Graph Theory. Reading, MA: Addison Wesley, first edition, 1971.Google Scholar
  16. 16.
    Jon Kleinberg and Eva Tardos. Algorithm Design. Reading, MA: Addison Wesley, first edition, 2006.Google Scholar
  17. 17.
    James R. Munkres. Elements of Algebraic Topology. Reading, MA: Addison-Wesley, first edition, 1984.Google Scholar
  18. 18.
    Christos H. Papadimitriou and Kenneth Steiglitz. Combinatorial Optimization. Algorithms and Complexity.New York: Dover, first edition, 1998.MATHGoogle Scholar
  19. 19.
    N. Robertson, D. Sanders, P.D. Seymour and R. Thomas. The four-color theorem. J. Combin. Theory B, 70:2–44, 1997.MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Michel Sakarovitch. Optimisation Combinatoire, Méthodes mathématiques et algorithmiques. Graphes et Programmation Linéaire. Paris: Hermann, first edition, 1984.MATHGoogle Scholar
  21. 21.
    Michel Sakarovitch. Optimisation Combinatoire, Méthodes mathématiques et algorithmiques. Programmation Discréte. Paris: Hermann, first edition, 1984.MATHGoogle Scholar
  22. 22.
    Herbert S. Wilf. Algorithms and Complexity. Wellesley, MA: A K Peters, second edition, 2002.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Computer and Information ScienceUniversity of PennsylvaniaPhiladelphiaUSA

Personalised recommendations