The Ramsey Numbers of Large cycles Versus Odd Wheels

Surahmat,; Baskoro, Edy Tri; Tomescu, Ioan

doi:10.1007/s00373-007-0764-6

Cited by 17 publications

(7 citation statements)

References 8 publications

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“…Theorem 4(a) was conjectured in a few papers by Surahmat et al [SuBT1,SuBT2,Sur]. Parts of this conjecture were proved in [SuBT1,ZhaCC], and the proof was completed by Chen, Cheng and Ng [ChenCN] in 2009.…”

Section: Cycles Versus Wheelsmentioning

confidence: 87%

Ramsey Numbers Involving Cycles

Radziszowski

2011

Ramsey Theory

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Section: Cycles Versus Wheelsmentioning

confidence: 87%

Ramsey Numbers Involving Cycles

Radziszowski

2011

Ramsey Theory

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“…For large cycles versus even wheels, Surahmat et al [22] determined that R(C m , W n ) = 3m − 2 for odd n ≥ 5 and m > (5n − 9)/2. This result was improved by Shi [18] who showed that R(C m , W n ) = 3m − 2 for odd n and m ≥ 3n/2 + 1.…”

Section: Theorem 2 (Burr and Erdősmentioning

confidence: 99%

Three Results on Cycle-Wheel Ramsey Numbers

Zhang

Broersma

Chen

2015

Graphs and Combinatorics

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Given two graphs G 1 and G 2 , the Ramsey number R(G 1 , G 2 ) is the smallest integer N such that, for any graph G of order N , either G 1 is a subgraph of G, or G 2 is a subgraph of the complement of G. We consider the case that G 1 is a cycle and G 2 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 versus cycles of even order; and large cycles versus generalized odd wheels.

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“…For instance Burr and Erdős [2] showed that R(C 3 , W n ) = 2n + 1 for n ≥ 5, Radziszowski and Xia [11] gave a method for counting the Ramsey numbers R(C 3 , G), where G is either a path, a cycle or a wheel. Surahmat et al [15,16,17] showed that R(C n , W m ) = 2n − 1 for even m and n ≥ 5m/2 − 1 and R(C n , W m ) = 3n − 2 for odd m and n > (5m − 9)/2. Zhang et al [19] The aim of this paper is to improve some results by reducing the lower bound for n. Also we will establish Ramsey numbers for some new graphs versus paths or cycles.…”

Section: Introductionmentioning

confidence: 99%

The Ramsey numbers for some subgraphs of generalized wheels versus cycles and paths

Bielak

Dąbrowska

2015

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The Ramsey number \(R(G, H)\) for a pair of graphs \(G\) and \(H\) is defined as the smallest integer \(n\) such that, for any graph \(F\) on \(n\) vertices, either \(F\) contains \(G\) or \(\overline{F}\) contains \(H\) as a subgraph, where \(\overline{F}\) denotes the complement of \(F\). We study Ramsey numbers for some subgraphs of generalized wheels versus cycles and paths and determine these numbers for some cases. We extend many known results studied in [5, 14, 18, 19, 20]. In particular we count the numbers \(R(K_1+L_n, P_m)\) and \(R(K_1+L_n, C_m)\) for some integers \(m\), \(n\), where \(L_n\) is a linear forest of order \(n\) with at least one edge.

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The Ramsey Numbers of Large cycles Versus Odd Wheels

Cited by 17 publications

References 8 publications

Ramsey Numbers Involving Cycles

Ramsey Numbers Involving Cycles

Three Results on Cycle-Wheel Ramsey Numbers

The Ramsey numbers for some subgraphs of generalized wheels versus cycles and paths

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