Skip to main content Accessibility help
×
Home

RAMSEY NUMBERS FOR TREES

  • ZHI-HONG SUN (a1)

Abstract

For n≥5, let Tn denote the unique tree on n vertices with Δ(Tn)=n−2, and let T*n=(V,E) be the tree on n vertices with V ={v0,v1,…,vn−1} and E={v0v1,…,v0vn−3,vn−3vn−2,vn−2vn−1}. In this paper, we evaluate the Ramsey numbers r(Gm,Tn) and r(Gm,T*n) , where Gm is a connected graph of order m. As examples, for n≥8 we have r(Tn,T*n)=r(T*n,T*n)=2n−5 , for n>m≥7 we have r(K1,m−1,T*n)=m+n−3 or m+n−4 according to whether m−1∣n−3 or m−1∤n−3 , and for m≥7 and n≥(m−3)2 +2 we have r(T*m,T*n)=m+n−3 or m+n−4 according to whether m−1∣n−3 or m−1∤n−3 .

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      RAMSEY NUMBERS FOR TREES
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      RAMSEY NUMBERS FOR TREES
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      RAMSEY NUMBERS FOR TREES
      Available formats
      ×

Copyright

References

Hide All
[1]Burr, S. A., ‘Generalized Ramsey theory for graphs—a survey’, in: Graphs and Combinatorics, Lecture Notes in Mathematics, 406 (eds. Bari, R.A. and Harary, F.) (Springer, Berlin–New York, 1974), pp. 5275.
[2]Burr, S. A. and Roberts, J. A., ‘On Ramsey numbers for stars’, Util. Math. 4 (1973), 217220.
[3]Erdős, P. and Gallai, T., ‘On maximal paths and circuits in graphs’, Acta Math. Acad. Sci. Hungar. 10 (1959), 337356.
[4]Fan, G. H. and Sun, L. L., ‘The Erdős–Sós conjecture for spiders’, Discrete Math. 307 (2007), 30553062.
[5]Faudree, R. J. and Schelp, R. H., ‘Path Ramsey numbers in multicolorings’, J. Combin. Theory Ser. B 19 (1975), 150160.
[6]Guo, Y. B. and Volkmann, L., ‘Tree-Ramsey numbers’, Aust. J. Combin. 11 (1995), 169175.
[7]Hua, L. K., Introduction to Number Theory (Springer, Berlin, 1982).
[8]Radziszowski, S. P., ‘Small Ramsey numbers’, Dynamic Surveys of Electronic J. Combinatorics (2011), DS1.13, 84 pp.
[9]Sidorenko, A. F., ‘Asymptotic solution for a new class of forbidden r-graphs’, Combinatorica 9 (1989), 207215.
[10]Sun, Z. H. and Wang, L. L., ‘Turán’s problem for trees’, J. Combin. Number Theory 3 (2011), 5169.
[11]Woźniak, M., ‘On the Erdős–Sós conjecture’, J. Graph Theory 21 (1996), 229234.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Keywords

MSC classification

RAMSEY NUMBERS FOR TREES

  • ZHI-HONG SUN (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed