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.
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J. Eckhoff, Intersection properties of boxes. I. An upper-bound theorem, Israel Journal of Mathematics 62 (1988), 283–301.
J. Eckhoff, The maximum number of triangles in a K 4-free graph, Discrete Mathematics 194 (1999), 95–106.
J. Eckhoff, A new Turán-type theorem for cliques in graphs, Discrete Mathematics 282 (2004), 113–122.
P. Frankl, Z. Füredi and G. Kalai, Shadows of colored complexes, Mathematica Scandinavica 63 (1988), 169–178.
G. Katona, A theorem of finite sets, in Theory of Graphs, Academic Press, New York, 1968, pp. 187–207.
J. B. Kruskal, The number of simplices in a complex, in Mathematical Optimization Techniques, University of California Press, Berkeley, California, 1963, pp. 251–278.
R. Stanley, Balanced Cohen-Macaulay complexes, Transactions of the American Mathematical Society 249 (1979), 139–157.
R. Stanley, Combinatorics and Commutative Algebra, Second Edition, Birkhauser Boston, Inc., Boston, Massachusetts, 1996.
P. Turán, Eine Extremalaufgabe aus der Graphentheorie Matematicheskaya Fizika, Lapok 48 (1941), 436–452.
A. A. Zykov, On some properties of linear complexes, American Mathematical Society Translations, 1952 no. 79.
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Frohmader, A. Face vectors of flag complexes. Isr. J. Math. 164, 153–164 (2008). https://doi.org/10.1007/s11856-008-0024-3
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DOI: https://doi.org/10.1007/s11856-008-0024-3