Israel Journal of Mathematics

, Volume 164, Issue 1, pp 153–164 | Cite as

Face vectors of flag complexes

Article
Received:

Abstract

A conjecture of Kalai and Eckhoff that the face vector of an arbitrary flag complex is also the face vector of some particular balanced complex is verified.

Keywords

Simplicial Complex Chromatic Number Canonical Representation Clique Number Balance Complex 
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.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    J. Eckhoff, Intersection properties of boxes. I. An upper-bound theorem, Israel Journal of Mathematics 62 (1988), 283–301.CrossRefMathSciNetMATHGoogle Scholar
  2. [2]
    J. Eckhoff, The maximum number of triangles in a K 4-free graph, Discrete Mathematics 194 (1999), 95–106.CrossRefMathSciNetMATHGoogle Scholar
  3. [3]
    J. Eckhoff, A new Turán-type theorem for cliques in graphs, Discrete Mathematics 282 (2004), 113–122.CrossRefMathSciNetMATHGoogle Scholar
  4. [4]
    P. Frankl, Z. Füredi and G. Kalai, Shadows of colored complexes, Mathematica Scandinavica 63 (1988), 169–178.MathSciNetMATHGoogle Scholar
  5. [5]
    G. Katona, A theorem of finite sets, in Theory of Graphs, Academic Press, New York, 1968, pp. 187–207.Google Scholar
  6. [6]
    J. B. Kruskal, The number of simplices in a complex, in Mathematical Optimization Techniques, University of California Press, Berkeley, California, 1963, pp. 251–278.Google Scholar
  7. [7]
    R. Stanley, Balanced Cohen-Macaulay complexes, Transactions of the American Mathematical Society 249 (1979), 139–157.CrossRefMathSciNetMATHGoogle Scholar
  8. [8]
    R. Stanley, Combinatorics and Commutative Algebra, Second Edition, Birkhauser Boston, Inc., Boston, Massachusetts, 1996.MATHGoogle Scholar
  9. [9]
    P. Turán, Eine Extremalaufgabe aus der Graphentheorie Matematicheskaya Fizika, Lapok 48 (1941), 436–452.MATHGoogle Scholar
  10. [10]
    A. A. Zykov, On some properties of linear complexes, American Mathematical Society Translations, 1952 no. 79.Google Scholar

Copyright information

© The Hebrew University of Jerusalem 2008

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA

Personalised recommendations