A note on Ramsey numbers for fans

Yanbo Zhang; Haitze J. Broersma; Yaojun Chen

doi:10.1017/S0004972715000398

A note on Ramsey numbers for fans

Yanbo Zhang
, Haitze J. Broersma
, Yaojun Chen

Research output: Contribution to journal › Article › Academic › peer-review

7 Citations (Scopus)

183 Downloads (Pure)

Abstract

For two given 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 G contains G1 as a subgraph or the complement of G contains G2 as a subgraph. A fan Fl is l triangles sharing exactly one vertex. In this note, it is shown that R(Fn, Fm) = 4n + 1 for n ≥ max{m 2 − m/2, 11m/2 − 4}.

Original language	English
Pages (from-to)	19-23
Number of pages	5
Journal	Bulletin of the Australian Mathematical Society
Volume	92
Issue number	1
DOIs	https://doi.org/10.1017/S0004972715000398
Publication status	Published - Aug 2015

Keywords

MSC-05C
Ramsey number
Fan
2024 OA procedure

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10.1017/S0004972715000398

ArticleFinal published version, 97.4 KBLicence: Taverne

Cite this

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title = "A note on Ramsey numbers for fans",

abstract = "For two given 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 G contains G1 as a subgraph or the complement of G contains G2 as a subgraph. A fan Fl is l triangles sharing exactly one vertex. In this note, it is shown that R(Fn, Fm) = 4n + 1 for n ≥ max\{m 2 − m/2, 11m/2 − 4\}.",

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KW - MSC-05C

KW - Ramsey number

KW - Fan

KW - 2024 OA procedure

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DO - 10.1017/S0004972715000398

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A note on Ramsey numbers for fans

Abstract

Keywords

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