منابع مشابه
On the Ramsey number of the quadrilateral versus the book and the wheel
Let G and H be graphs. The Ramsey number R(G, H) is the least integer such that for every graph F of order R(G, H), either F contains G or F contains H . Let Bn and Wn denote the book graph K2 +Kn and the wheel graph K1 + Cn−1, respectively. In 1978, Faudree, Rousseau and Sheehan computed R(C4, Bn) for n ≤ 8. In this paper, we compute R(C4, Bn) for 8 ≤ n ≤ 12 and R(C4, Wn) for 4 ≤ n ≤ 13. In pa...
متن کاملThree Results on Cycle-Wheel Ramsey Numbers
Given twographsG1 andG2, theRamseynumber R(G1,G2) is the smallest integer N such that, for any graph G of order N , either G1 is a subgraph of G, or G2 is a subgraph of the complement of G. We consider the case that G1 is a cycle and G2 is a (generalized) wheel. We expand the knowledge on exact values of Ramsey numbers in three directions: large cycles versus wheels of odd order; large wheels v...
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 کاملA remark on star-C4 and wheel-C4 Ramsey numbers
Given two graphs G1 and G2, the Ramsey number R(G1, G2) is the smallest integer N such that, for any graph G of order N , either G1 is a subgraph of G, or G2 is a subgraph of the complement of G. Let Cn denote a cycle of order n, Wn a wheel of order n + 1 and Sn a star of order n. In this paper, it is shown that R(Wn, C4) = R(Sn+1, C4) for n ≥ 6. Based on this result and Parsons’ results on R(S...
متن کاملA note on the Ramsey number and the planar Ramsey number for C4 and complete graphs
We give a lower bound for the Ramsey number and the planar Ramsey number for C4 and complete graphs. We prove that the Ramsey number for C4 and K7 is 21 or 22. Moreover we prove that the planar Ramsey number for C4 and K6 is equal to 17.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2000
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(00)00049-2