Skip to main content
Springer Nature Link
Log in

Nonexistence of universal graphs without some trees

  • Published:
Combinatorica Aims and scope Submit manuscript

Abstract

IfG is a finite tree with a unique vertex of largest, and ≥4 degree which is adjacent to a leaf then there is no universal countableG-free graph.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. B. Bollobás:Random graphs, 1985, Academic Press.

  2. P. A. Catlin: Subgraphs of graphs I,Discrete Mathematics,10 (1974), 225–233.

    Google Scholar 

  3. G. Cherlin, P. Komjáth: There is no universal countable pentagon free graph,Journal of Graph Theory,18 (1994), 337–341.

    Google Scholar 

  4. G. Cherlin, N. Shi: Graphs omitting sums of complete graphs,Journal of Graph Th.,24 (1997), 237–247.

    Google Scholar 

  5. G. Cherlin, N. Shi: Graphs omitting a finite set of cycles,Journal of Graph Theory,21 (1996), 351–355.

    Google Scholar 

  6. Z. Füredi, P. Komjáth: On the existence of countable universal graphs,Journal of Graph Th.,25 (1997), 53–58.

    Google Scholar 

  7. M. Goldstern, M. Kojman: Universal arrow-free graphs,Acta Math. Hung,73 (1996), 319–326.

    Google Scholar 

  8. A. Hajnal, J. Pach: Monochromatic paths in infinite graphs, in:Finite and Infinite sets, Coll. Math. Soc. J. Bolyai,37, (Eger, Hungary, 1981), 359–369.

  9. P. Komjáth, A. Mekler, J. Pach: Some universal graphs,Israel Journal of Mathematics,64 (1988), 158–168.

    Google Scholar 

  10. P. Komjáth, J. Pach: Universal graphs without large bipartite graphs,Mathematika,31 (1984), 282–290.

    Google Scholar 

  11. P. Komjáth, J. Pach: Universal elements and the complexity of certain classes of infinite graphs,Discrete Math. 95 (1991), 255–270.

    Google Scholar 

  12. P. Komjáth, J. Pach: The complexity of a class of infinite graphs,Combinatorica,14 (1994), 121–125.

    Google Scholar 

  13. R. Rado: Universal graphs and universal functions,Acta Arith,9 (1964), 331–340.

    Google Scholar 

  14. R. Rado: Universal graphs, inA Seminar in Graph Theory, (eds. Harary, Beineke), Holt, Rinehart, and Winston Co., 1967.

  15. V. Rödl, L. Thoma: The complexity of cover graph recognition for some varieties of finite lattices,to appear.

  16. N. Sauer, J. Spencer: Edge disjoint placement of graphs,Journal of Combinatorial Theory (B),25 (1978), 295–302.

    Google Scholar 

  17. G. Cherlin, N. Shi, andL. Talggren: Graphs omitting a bushy tree,Journal of Graph Th., to appear.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green St., 61801-2917, Urbana, IL, USA

    Z. Füredi

  2. Mathematical Institute of the Hungarian Academy of Sciences, P.O.Box 127, 1364, Budapest, Hungary

    Z. Füredi

  3. Department of Computer Science, Eötvös University, Múzeum krt. 6-8, 1088, Budapest, Hungary

    P. Komjáth

Authors
  1. Z. Füredi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Komjáth
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research partially supported by the Hungarian Science Research Grant OTKA No. 2117 and by the European Communities (Cooperation in Science and Technology with Central and Eastern European Countries) contract number ERBCIPACT930113.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Füredi, Z., Komjáth, P. Nonexistence of universal graphs without some trees. Combinatorica 17, 163–171 (1997). https://doi.org/10.1007/BF01200905

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01200905

Mathematics Subject Classification (1991)