Zhang, Yanbo; Broersma, Hajo; Chen, Yaojun A note on Ramsey numbers for fans. (English) Zbl 1319.05134 Bull. Aust. Math. Soc. 92, No. 1, 19-23 (2015). Summary: For two given 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 \(G\) contains \(G_{1}\) as a subgraph or the complement of \(G\) contains \(G_{2}\) as a subgraph. A fan \(F_{l}\) is \(l\) triangles sharing exactly one vertex. In this note, it is shown that \(R(F_{n},F_{m})=4n+1\) for \(n\geq \max \{m^{2}-m/2,11m/2-4\}\). Cited in 1 ReviewCited in 4 Documents MSC: 05D10 Ramsey theory 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) Keywords:Ramsey number; fan; goodness PDFBibTeX XMLCite \textit{Y. Zhang} et al., Bull. Aust. Math. Soc. 92, No. 1, 19--23 (2015; Zbl 1319.05134) Full Text: DOI References: [1] Hall, J. Lond. Math. Soc. (2) 10 pp 26– (1935) [2] DOI: 10.2140/pjm.1972.41.335 · Zbl 0227.05115 · doi:10.2140/pjm.1972.41.335 [3] DOI: 10.1112/jlms/s2-24.3.405 · Zbl 0474.05051 · doi:10.1112/jlms/s2-24.3.405 [4] DOI: 10.1016/j.ejc.2009.10.011 · Zbl 1205.05157 · doi:10.1016/j.ejc.2009.10.011 [5] DOI: 10.1016/j.dam.2008.05.004 · Zbl 1159.05034 · doi:10.1016/j.dam.2008.05.004 [6] DOI: 10.1002/(SICI)1097-0118(199612)23:4<413::AID-JGT10>3.0.CO;2-D · Zbl 0954.05031 · doi:10.1002/(SICI)1097-0118(199612)23:4<413::AID-JGT10>3.0.CO;2-D This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.