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On the Divisibility of Homogeneous Directed Graphs

Published online by Cambridge University Press:  20 November 2018

M. El-Zahar  and
N. W. Sauer
M. El-Zahar
Affiliation:
Department of Mathematics, University of Calgary, Calgary, Alberta, T2N 1N4
N. W. Sauer
Affiliation:
Department of Mathematics, University of Calgary, Calgary, Alberta, T2N 1N4
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Abstract

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Let be a finite set of finite tournaments. We will give a necessary and sufficient condition for the -free homogeneous directed graph to be divisible. That is, that there is a partition of into two classes such that neither of them contains an isomorphic copy of .

Keywords

06A1005C2020B27homogeneous structuresindivisibilitydirected graphs
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 2 , 01 April 1993 , pp. 284 - 294
Copyright
Copyright © Canadian Mathematical Society 1993

References

1. Cherlin, G., Homogeneous directed graphs, the imprimitive case, Logic colloquium 85, Elsevier, North– Holland, 1987.Google Scholar
2. El–Zahar, M. and Sauer, N.W., The indivisibility of the homogeneous Kn-free graphs, Journal of Combinatorial Theory B (2) 47, 1989.Google Scholar
3. Folkman, J., Graphs with monochromatic complete subgraphs in every edgecoloring, SIAM J. Appl. Math. 18(1970), 115–124.Google Scholar
4. Fraissé, R., Theory of Relations, Studies in Logic and the Foundations of Mathematics, Elsevier Science Publishing Co., Inc., U.S.A. 118(1986).Google Scholar
5. Henson, C.W., Countable homogeneous relational structures and N0-categorical theories, J. Symbolic Logic 37(1972), 494–500.Google Scholar
6. Komjâth, P. and Rôdl, V., Coloring ofUnviersal Graphs, Graphs and Combinatorics 2(1986), 55–60.Google Scholar
7. Lachlan, A.H., Countable Homogeneous Tournaments, Trans. Amer. Math. Soc. 284(1984), 431–461.Google Scholar
8. Lachlan, A.H. and Woodrow, R.E., Countable Ultrahomogeneous Undirected Graphs, Transactions of the American Mathematical Society (1) 262, 1980.Google Scholar
9. Petetyiatkin, M.G., On complete theories with a finite number of denumerable models, Algebra; Logika 12(1973), 550–576.Google Scholar
10. Pouzet, M., Relations impartibles, Dissertationes Matimaticae CXCIII, Warszawa, 1981.Google Scholar
11. Schmerl, J.H., Countable homogeneous partially ordered sets, Algebra Universalis, 9(1979), 317–321.Google Scholar