Borowiecki, M.; Schiermeyer, I.; Sidorowicz, E. Ramsey \((K_ {1,2},K_ 3)\)-minimal graphs. (English) Zbl 1081.05071 Electron. J. Comb. 12, No. 1, Research paper 20, 15 p. (2005). If \(G,F\) and \(H\) are arbitrary graphs then the notation \(G\rightarrow(F,H)\) means, that for any 2-colouring of the edges of \(G\) either the first colour contains a copy of \(F\) or \(H\) is a subgraph of the graph induced by the second colour. A graph \(G\) is called \((F,H)\)-Ramsey-minimal if \(G\rightarrow(F,H)\) but \(G^*\not\rightarrow(F,H)\) for any proper subgraph \(G^*\) of \(G\). The class of all \((F,H)\)-Ramsey minimal graphs is denoted by \(R(F,H)\).The paper contains a complete characterisation of the class \(R(K_{1,2},K_3)\). The proof of the main result is based on a few structural lemmas that provide necessary conditions for the graphs belonging to \(R(K_{1,2},K_3)\). Reviewer: Gabriel Semanišin (Košice) Cited in 5 Documents MSC: 05C55 Generalized Ramsey theory Keywords:generalised Ramsey number PDFBibTeX XMLCite \textit{M. Borowiecki} et al., Electron. J. Comb. 12, No. 1, Research paper 20, 15 p. (2005; Zbl 1081.05071) Full Text: EuDML EMIS