منابع مشابه
On cycle - Complete graph ramsey numbers
A new upper bound is given for the cycle-complete graph Ramsey number r(C,,,, K„), the smallest order for a graph which forces it to contain either a cycle of order m or a set of ri independent vertices . Then, another cycle-complete graph Ramsey number is studied, namely r( :C,,,, K„) the smallest order for a graph which forces it to contain either a cycle of order 1 for some I satisfying 3 :1...
متن کاملThe Cycle-Complete Graph Ramsey Numbers
In 1978 Erdős, Faudree, Rousseau, and Schelp conjectured that r (Cp, Kr) = (p − 1) (r − 1) + 1. for every p ≥ r ≥ 3, except for p = q = 3. This has been proved for r ≤ 6, and for p ≥ r 2 − 2r. In this note we prove the conjecture for p ≥ 4r + 2.
متن کاملBook Ramsey numbers. I
A book Bp is a graph consisting of p triangles sharing a common edge. In this paper we prove that if p ≤ q/6 − o (q) and q is large then the Ramsey number r (Bp, Bq) is given by r (Bp, Bq) = 2q + 3 and the constant 1/6 is essentially best possible. Our proof is based on Szemerédi’s uniformity lemma and a stability result for books.
متن کاملOn a conjecture involving cycle-complete graph Ramsey numbers
It has been conjectured that r(Cnl Km) = (m 1)(n 1) + 1 for all (n, m) =1= (3,3) satisfying n ~ m. We prove this for the case m = 5. * This author is currently pursuing post-doctoral studies under Prof. Bollobas Australasian Journal of Combinatorics 22(2000), pp.63-71
متن کاملA Note on Odd Cycle-Complete Graph Ramsey Numbers
The Ramsey number r(Cl,Kn) is the smallest positive integer m such that every graph of order m contains either cycle of length l or a set of n independent vertices. In this short note we slightly improve the best known upper bound on r(Cl,Kn) for odd l.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1996
ISSN: 0095-8956
DOI: 10.1006/jctb.1996.0055