The Ramsey numbers for cycles versus wheels of odd order

Yaojun Chen; Edwin Tai Chiu Cheng; Zhengke Miao; Chi To Ng

doi:10.1016/j.aml.2009.07.014

The Ramsey numbers for cycles versus wheels of odd order

Yaojun Chen, Edwin Tai Chiu Cheng, Zhengke Miao, Chi To Ng

Research output: Journal article publication › Journal article › Academic research › peer-review

6 Citations (Scopus)

Abstract

For two given graphs G1and G2, the Ramsey number R (G1, G2) is the smallest integer n such that for any graph G of order n, either G contains G1or the complement of G contains G2. Let Cndenote a cycle of order n and Wma wheel of order m + 1. It is conjectured by Surahmat, E.T. Baskoro and I. Tomescu that R (Cn, Wm) = 2 n - 1 for even m ≥ 4, n ≥ m and (n, m) ≠ (4, 4). In this paper, we confirm the conjecture for n ≥ 3 m / 2 + 1.

Original language	English
Pages (from-to)	1875-1876
Number of pages	2
Journal	Applied Mathematics Letters
Volume	22
Issue number	12
DOIs	https://doi.org/10.1016/j.aml.2009.07.014
Publication status	Published - 1 Dec 2009

Keywords

Cycle
Ramsey number
Wheel

ASJC Scopus subject areas

Applied Mathematics

More information

10.1016/j.aml.2009.07.014

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abstract = "For two given graphs G1and G2, the Ramsey number R (G1, G2) is the smallest integer n such that for any graph G of order n, either G contains G1or the complement of G contains G2. Let Cndenote a cycle of order n and Wma wheel of order m + 1. It is conjectured by Surahmat, E.T. Baskoro and I. Tomescu that R (Cn, Wm) = 2 n - 1 for even m ≥ 4, n ≥ m and (n, m) ≠ (4, 4). In this paper, we confirm the conjecture for n ≥ 3 m / 2 + 1.",

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AU - Chen, Yaojun

AU - Cheng, Edwin Tai Chiu

AU - Miao, Zhengke

AU - Ng, Chi To

PY - 2009/12/1

Y1 - 2009/12/1

N2 - For two given graphs G1and G2, the Ramsey number R (G1, G2) is the smallest integer n such that for any graph G of order n, either G contains G1or the complement of G contains G2. Let Cndenote a cycle of order n and Wma wheel of order m + 1. It is conjectured by Surahmat, E.T. Baskoro and I. Tomescu that R (Cn, Wm) = 2 n - 1 for even m ≥ 4, n ≥ m and (n, m) ≠ (4, 4). In this paper, we confirm the conjecture for n ≥ 3 m / 2 + 1.

AB - For two given graphs G1and G2, the Ramsey number R (G1, G2) is the smallest integer n such that for any graph G of order n, either G contains G1or the complement of G contains G2. Let Cndenote a cycle of order n and Wma wheel of order m + 1. It is conjectured by Surahmat, E.T. Baskoro and I. Tomescu that R (Cn, Wm) = 2 n - 1 for even m ≥ 4, n ≥ m and (n, m) ≠ (4, 4). In this paper, we confirm the conjecture for n ≥ 3 m / 2 + 1.

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KW - Ramsey number

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JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

IS - 12

ER -

The Ramsey numbers for cycles versus wheels of odd order

Abstract

Keywords

ASJC Scopus subject areas

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