On the Existence of Countable Universal Graphs

Journal of Graph Theory

Volumn 25, Issue 1, 1997, Pages 53-58

  Füredi, Zoltán ^a   Komjáth, Péter ^b  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b EÖTVÖS LORÁND UNIVERSITY   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0345812332     PISSN: 03649024     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0118(199705)25:1<53::AID-JGT3>3.3.CO;2-U     Document Type: Article

References (18)

1. N. Alon and J. Spencer, The probabilistic method, Wiley-Interscience, New York (1992).
2. B. Bollobás, Extremal graph theory, Academic Press, London (1978).
3. G. Cherlin and P. Komjáth, There is no universal countable pentagon free graph, J. Graph Theory 18 (1994), 337-342.
4. G. Cherlin and N. Shi, Graphs omitting a finite set of cycles, J. Graph Theory 21 (1996), 351-355.
5. P. Erdos and H. Sachs, Reguläre Graphen gegebener Taillenweite mit minimaler Knotenzahl, Wiss. Z. Univ. Halle Martin-Luther Univ. Halle-Wittenberg Math.-Natur. Reihe 12 (1963), 251-257.
6. Z. Füredi and P. Komjáth, Nonexistence of universal graphs without some trees, to appear.
7. Z. Füredi, F. Lazebnik, Á. Seress, V. A. Ustimenko, and A. J. Woldar, Graphs of prescribed girth and bi-degree, J. Combinatorial Theory, Ser. B 64 (1995), 228-239.
8. M. Goldstern and M. Kojman, Bridges are not universal, to appear.
9. A. Hajnal and J. Pach, Monochromatic paths in infinite graphs, in: Finite and infinite sets, Proc. Colloq. Soc. J. Bolyai 37 (1981), 359-369. North-Holland, Amsterdam.
10. P. Komjáth, A. Mekler, and J. Pach, Some universal graphs, Israel J. Math. 64 (1988), 158-168.
11. P. Komjáth and J. Pach, Universal graphs without large bipartite graphs, Mathematika 31 (1984), 282-290.
12. P. Komjáth and J. Pach, Universal elements and the complexity of certain classes of infinite graphs, Discrete Math. 95 (1991), 255-270.
13. P. Komjáth and J. Pach, The complexity of a class of infinite graphs, Combinatorica 14 (1994), 121-125.
14. P. Komjáth and S. Shelah, Universal graphs without large cliques, J. Combin. Theory Ser. B 63 (1995), 125-135.
15. L. Lovász, Combinatorial problem and exercises, North-Holland and Akadémiai Kaidó, Amsterdam and Budapest (1979).
16. R. Rado, Universal graphs and universal functions, Acta Arithmetica 9 (1964), 331-340.
17. R. Rado, Universal graphs, in: A Seminar in graph theory, pp. 83-85. (F. Harary and L. W. Beineke, Eds.), Holt, Rinehart and Winston, New York (1967).
18. R. Fraïssé: sur l'extension aux relations de quelques propriétés connues des ordres, C. R. Acad Sci. Paris 237 (1953), 508-510. MR 15-192.