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

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Hałuszczak M.

Discussiones Mathematicae Graph Theory

2012

tom 32

nr 2

331-339

Let F be a graph and let 𝓖,𝓗 denote nonempty families of graphs. We write F → (𝓖,𝓗) if in any 2-coloring of edges of F with red and blue, there is a red subgraph isomorphic to some graph from G or a blue subgraph isomorphic to some graph from H. The graph F without isolated vertices is said to be a (𝓖,𝓗)-minimal graph if F → (𝓖,𝓗) and F - e not → (𝓖,𝓗) for every e ∈ E(F). We present a technique which allows to generate infinite family of (𝓖,𝓗)-minimal graphs if we know some special graphs. In particular, we show how to receive infinite family of $(K_{1,2}, Kₙ)$-minimal graphs, for every n ≥ 3.

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1 Discussiones Mathematicae Graph Theory

1 Hałuszczak M.

1 2012

Wyniki wyszukiwania

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