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A Theorem on Countable Ordered Sets with an Application to Universal Graphs

Published online by Cambridge University Press:  31 March 2017

Péter Komjáth
Affiliation:
Calgary University, Calgary, Alberta, Canada
Samuel R. Buss
Affiliation:
University of California, San Diego
Petr Hájek
Affiliation:
Academy of Sciences of the Czech Republic, Prague
Pavel Pudlák
Affiliation:
Academy of Sciences of the Czech Republic, Prague
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Logic Colloquium '98 , pp. 296 - 301
Publisher: Cambridge University Press
Print publication year: 2000

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References

1. Cherlin, G. Shelah, S. Shi|N. Universal graphs with forbidden graphs and algebraic closure, (to appear)
2. Cherlin, G. Shi, N.: Graphs omitting sums of complete graphs. Journal of Graph Theory 24 (1997) 237–247Google Scholar
3. Cherlin, G. Shi, N. Tallgren|L. Graphs omitting a bushy tree. Journal of Graph Theory 26 (1997) 203–210Google Scholar
4. Erdʺos, P. Hajnal, A.:On a classification of denumerable order types and an application to the partition calculus. Fundamenta Mathematicae 51 (1962) 117–129Google Scholar
5. Füredi, Z. Komjáth, P. :On the existence of countable universal graphs. Journal of Graph Theory 25 (1997) 53–58Google Scholar
6. Füredi, Z. Komjáth, P.:Nonexistence of universal graphs without some trees. Combinatorica 17 (1997) 163–171Google Scholar
7. Hausdorff, F.:Grundzüge einer Theorie der GeordneteMengen.Math.Ann. 65 (1908) 435–505Google Scholar
8. Komjáth, P. Pach, J.: Universal elements and the complexity of certain classes of infinite graphs. Discrete Math. 95 (1991) 255–270Google Scholar
9. Komjáth, P. Shelah, S.|: Universal graphs without large cliques, J.Comb. Th (B) (1995) 125–135
10. Laver, R.: On Fraıssé's order type conjecture. Ann. Math. 93 (1971) 89–111Google Scholar
11. Rado, R.: Universal graphs and universal functions. Acta Arithmetica 9 (1964) 331–340.Google Scholar
12. Rado, R.: Universal graphs, in: A seminar in graph theory, (Harary and Beineke, eds.), Holt, Rinehart and Winston Co., 1967
13. Joseph G., Rosenstein: Linear orderings, Academic Press, 1982.

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