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Forbidden subgraphs and forbidden substructures

Published online by Cambridge University Press:  12 March 2014

Gregory Cherlin  and
Niandong Shi
Gregory Cherlin
Affiliation:
Department of Mathematics, Rutgers University, Busch Campus, Piscataway, NJ 08854, USA
Niandong Shi
Affiliation:
Department of Mathematics, East Stroudsburg University, East Stroudsburg, PA 18301, USA, E-mail: [email protected]
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Abstract

The problem of the existence of a universal structure omitting a finite set of forbidden substructures is reducible to the corresponding problem in the category of graphs with a vertex coloring by two colors. It is not known whether this problem reduces further to the category of ordinary graphs. It is also not known whether these problems are decidable.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 3 , September 2001 , pp. 1342 - 1352
Copyright
Copyright © Association for Symbolic Logic 2001

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References

REFERENCES

[CSS]Cherlin, G., Shelah, S., and Shi, N., Universal graphs and algebraic closure, Advances in Applied Mathematics, vol. 22 (1999), pp. 454–491.CrossRefGoogle Scholar
[CS]Cherlin, G. and Shi, N., Graphs omitting a finite set of cycles, Journal of Graph Theory, vol. 21 (1996), pp. 351–355.3.0.CO;2-K>CrossRefGoogle Scholar
[FK]Füredi, Z. and Komjáth, P., On the existence of countable universal graphs, Journal of Graph Theory, vol. 25 (1997), pp. 53–58.3.0.CO;2-H>CrossRefGoogle Scholar
[KMW]Kahr, A. S., Moore, E. F., and Wang, H., Entscheidungsproblem reduced to the ∀∃∀ case, Proceedings of the National Academy of Sciences of the United States of America, vol. 48 (1962), pp. 365–377.CrossRefGoogle Scholar
[KMP]Komjáth, P., Mekler, A., and Pach, J., Some universal graphs, Israel Journal of Mathematics, vol. 64 (1988), pp. 158–168.CrossRefGoogle Scholar
[KP]Komjáth, P. and Pach, J., Universal elements and the complexity of certain classes of infinite graphs, Discrete Mathematics, vol. 95 (1991), pp. 255–270.CrossRefGoogle Scholar