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Experimental Mathematics Volume 17, 2008 - Issue 1
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Original Article

On the Folkman Number f(2, 3, 4)

Andrzej Dudek Department of Mathematics and Computer Science, Emory University, Mathematics and Science Center, 400 Dowman Drive, Atlanta, GA 30322
&
Vojtěch Rödl Department of Mathematics and Computer Science, Emory University, Mathematics and Science Center, 400 Dowman Drive, Atlanta, GA 30322
Pages 63-67 | Published online: 30 Jan 2011

  • F. Chung and R. Graham. Erdős on Graphs: His Legacy of Unsolved Problems. Wellesley: A K Peters, 1998.
  • A. Dudek. "Problems in Extremal Combinatorics." PhD thesis, Emory University, 2008.
  • P. Erdős. "Problems and Results in Finite and Infinite Graphs." In Recent Advances in Graph Theory (Proceedings of the Symposium Held in Prague), edited by M. Fiedler, pp. 183–192. Prague: Academia Praha, 1975.
  • J. Folkman. "Graphs with Monochromatic Complete Subgraphs in Every Edge Coloring." SIAM J. Appl. Math. 18 (1970), 19–24.
  • P. Frankl and V. Rödl. "Large Triangle- Free Subgraphs in Graphs without K4." Graphs and Combinatorics 2 (1986), 135–144.
  • A. Goodman. "On Sets of Acquaintances and Strangers at any Party." Amer. Math. Monthly 66 (1959), 778–783.
  • R. Graham. "On Edgewise 2-Colored Graphs with Monochromatic Triangles and Containing No Complete Hexagon." J. Comb. Theory 4 (1968), 300.
  • R. Hill and R. W. Irving. "On Group Partitions Associated with Lower Bounds for Symmetric Ramsey Numbers." European J. Combinatorics 3 (1982), 35–50.
  • R. Horn and C. Johnson. Matrix Analysis. Cambridge: Cambridge University Press, 1985.
  • M. Krivelevich and B. Sudakov. "Pseudo-random Graphs." In More Sets, Graphs and Numbers, pp. 199–262, Bolyai Society Mathematical Studies 15. New York: Springer, 2006.
  • L. Lu. "Explicit Construction of Small Folkman Graphs." To appear in SIAM Journal on Discrete Mathematics, 2008.
  • J. Nešetřil and V. Rödl. "The Ramsey Property for Graphs with Forbidden Complete Subgraphs." J. Comb. Theory Ser. B 20 (1976), 243–249.
  • K. Piwakowski, S. Radziszowski, and S. Urbański. "Computation of the Folkman Number Fe (3, 3; 5)." J. Graph Theory 32 (1999), 41–49.
  • S. Radziszowski and Xu Xiaodong. "On the Most Wanted Folkman Graph." Geombinatorics 16:4 (2007), 367–381.
  • F. Rendl, G. Rinaldi, and A. Wiegele. "Biq Mac Solver: Binary Quadratic and Max Cut Solver." Available online (http://biqmac.uni-klu.ac.at/), 2007. http://biqmac.uni-klu.ac.at/
  • F. Rendl, G. Rinaldi, and A. Wiegele. "A Branch and Bound Algorithm for Max-Cut Based on Combining Semidefinite and Polyhedral Relaxations." In Integer Programming and Combinatorial Optimization, pp. 295–309, Lecture Notes in Comput. Sci. 4513. New York: Springer, 2007.
  • J. Spencer. "Three Hundred Million Points Suffice." J. Comb. Theory Ser. A 49 (1988), 210–217. See also erratum by M. Hovey in ibid. 50 (1989), 323.

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