Skip to main content
×
Home
    • Aa
    • Aa
  • Bulletin of the Australian Mathematical Society, Volume 86, Issue 1
  • August 2012, pp. 164-176

RAMSEY NUMBERS FOR TREES

  • ZHI-HONG SUN (a1)
  • DOI: http://dx.doi.org/10.1017/S0004972711003388
  • Published online: 07 February 2012
Abstract
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 .

Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]S. A. Burr , ‘Generalized Ramsey theory for graphs—a survey’, in: Graphs and Combinatorics, Lecture Notes in Mathematics, 406 (eds. R.A. Bari and F. Harary ) (Springer, Berlin–New York, 1974), pp. 5275.

[3]P. Erdős and T. Gallai , ‘On maximal paths and circuits in graphs’, Acta Math. Acad. Sci. Hungar. 10 (1959), 337356.

[4]G. H. Fan and L. L. Sun , ‘The Erdős–Sós conjecture for spiders’, Discrete Math. 307 (2007), 30553062.

[5]R. J. Faudree and R. H. Schelp , ‘Path Ramsey numbers in multicolorings’, J. Combin. Theory Ser. B 19 (1975), 150160.

[9]A. F. Sidorenko , ‘Asymptotic solution for a new class of forbidden r-graphs’, Combinatorica 9 (1989), 207215.

[11]M. Woźniak , ‘On the Erdős–Sós conjecture’, J. Graph Theory 21 (1996), 229234.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords: