The Ramsey numbers for cycles versus wheels of even order

Lianmin Zhang; Yaojun Chen; Edwin Tai Chiu Cheng

doi:10.1016/j.ejc.2008.12.022

The Ramsey numbers for cycles versus wheels of even order

Lianmin Zhang
, Yaojun Chen
, Edwin Tai Chiu Cheng

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

13 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. Surahmat, Baskoro and Tomescu conjectured that R (Cn, Wm) = 3 n - 2 for m odd, n ≥ m ≥ 3 and (n, m) ≠ (3, 3). In this paper, we confirm the conjecture for n ≥ 20.

Original language	English
Pages (from-to)	254-259
Number of pages	6
Journal	European Journal of Combinatorics
Volume	31
Issue number	1
DOIs	https://doi.org/10.1016/j.ejc.2008.12.022
Publication status	Published - 1 Jan 2010

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

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10.1016/j.ejc.2008.12.022

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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. Surahmat, Baskoro and Tomescu conjectured that R (Cn, Wm) = 3 n - 2 for m odd, n ≥ m ≥ 3 and (n, m) ≠ (3, 3). In this paper, we confirm the conjecture for n ≥ 20.

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JF - European Journal of Combinatorics

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The Ramsey numbers for cycles versus wheels of even order

Abstract

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