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Generalized Ramsey theory VI: Ramsey numbers for small plexes

Published online by Cambridge University Press:  09 April 2009

Richard A. Duke  and
Frandk Harary
Richard A. Duke
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332, U.S.A.
Frandk Harary
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332, U.S.A.
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Abstract

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Generalized Ramsey theory for graphs was formulated and developed in the previous papers in this series. We extend the area here by introducing generalized Ramsey numbers for higher dimensional simplicial complexes. In particular we calculate explicitly the Ramsey numbers for several small “pure 2-complexes”, or more briefly plexes, in which each edge is contained in some 2–call.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 22 , Issue 4 , December 1976 , pp. 400 - 410
Copyright
Copyright © Australian Mathematical Society 1976

References

Burr, S. A. (1974), ‘Generalized Ramsey theory graphs — a survey’, Graphs and combinatorics (Bari, R. and Harary, F., eds.). (Springer-Verlag, Berlin, 52–75).CrossRefGoogle Scholar
Chvátal, V., Harary, F. (1972), ‘Generalized Ramsey theory for graphs’, Bull. Amer. Math. Soc. 78 423–426.CrossRefGoogle Scholar
Chvátal, V., Harary, F. (1972a), ‘Generalized Ramsey theory for graphs II, Small diagonal numbers’, Proc. Amer. Math. Soc. 32, 389–394.CrossRefGoogle Scholar
Chvátal, V., Harary, F. (1972b), ‘Generalized Ramsey theory for graphs III, Small off-diagonal numbers’, Pacific J. Math. 41, 335–345.CrossRefGoogle Scholar
Chvátal, V., Harary, F. (1973), ‘Generalized Ramsey theory for graphs I, Diagonal numbers’, Periodica Math. Huhgar. 3, 113–122.Google Scholar
Duke, R. A. (1975), ‘Ramsey numbers of families of 2-complexes’, (to appear).Google Scholar
Graver, J. E. and Yackel, J. (1968), ‘Some graph theoretic results associated with Ramsey's theorem’, J. Combinational Theory 4, 125–175.CrossRefGoogle Scholar
Hall, M. Jr, (1967), Combinatorial Theory (Blasidell, 1967).Google Scholar
Harary, F. (1955), ‘The number of linear, directed, rooted and connected graphs’, Trans. Amer. Math. Soc. 78, 445–463.CrossRefGoogle Scholar
Harary, F. (1969), Graph Theory (Addison-Wesley, 1969).CrossRefGoogle Scholar
Harary, F. (1974), ‘A survey of generalized Ramsey theory’, Graphs and Combinatorics (Bari, R. and Harary, F., eds.). (Springer-Verlag, Berlin, 1974), 10–17.CrossRefGoogle Scholar
Harary, F., Hell, P. (1974), ‘Generalized Ramsey theory for graphs V, The Ramsey number of a digraph’, Bull. London Math. Soc. 6, 175–182.CrossRefGoogle Scholar
Harary, F., Palmer, E. M. (1968), ‘On acyclic simplicial complexes’, Mathematika 15, (115–122).CrossRefGoogle Scholar
Harary, F., Prins, G. (1974), ‘Generalized Ramsey theory for graphs IV, The Ramsey multiplicity of a graph’, Networks 4, 163–173.CrossRefGoogle Scholar
Ramsey, F. P. (1930), ‘On a problem of formal logic’, Proc. London Math. Soc. 30, 264–286.CrossRefGoogle Scholar
Ryser, H. J. (1963), Combinatorial Mathematics. (Mathematical Association of America, 1963).CrossRefGoogle Scholar
Sobczyk, A. (1967), ‘Multi-functions associated with Steiner systems’, Notices Amer. Math. Soc. 14, 9–25.Google Scholar