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On Ramsey $(K_{1, 2}, C ₄)$ -minimal graphs

Tomás Vetrík; Lyra Yulianti; Edy Tri Baskoro — 2010

Discussiones Mathematicae Graph Theory

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 $(K_{1, 2}, C ₄)$ -minimal graphs of any diameter ≥ 4.

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On Ramsey ( K 1 , 2 , C ₄ ) -minimal graphs

On Ramsey $(K_{1, 2}, C ₄)$ -minimal graphs