Geodesic
On Ramsey $(K_{1,2},C₄)$-minimal graphs
Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 4, pp. 637-649

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For graphs F, G and H, we write F → (G,H) to mean that any red-blue coloring of the edges of F contains a red copy of G or a blue copy of H. The graph F is Ramsey (G,H)-minimal if F → (G,H) but F* ↛ (G,H) for any proper subgraph F* ⊂ F. We present an infinite family of Ramsey (K_1,2,C₄)-minimal graphs of any diameter ≥ 4.
Keywords: Ramsey-minimal graph, edge coloring, diameter of a graph 
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Vetrík, Tomás; Yulianti, Lyra; Baskoro, Edy. On Ramsey $(K_{1,2},C₄)$-minimal graphs. Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 4, pp. 637-649. http://geodesic.mathdoc.fr/item/DMGT_2010_30_4_a8/