Let F be a graph and let , denote nonempty families of graphs. We write F → (,) 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 (,)-minimal graph if F → (,) and F - e not → (,) for every e ∈ E(F). We present a technique which allows to generate infinite family of (,)-minimal graphs if we know some special graphs. In particular, we show how to receive infinite family of -minimal graphs, for every n ≥ 3.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1604,
author = {Mariusz Ha\l uszczak},
title = {On Ramsey $(K\_{1,2}, Kn)$-minimal graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {32},
year = {2012},
pages = {331-339},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1604}
}
Mariusz Hałuszczak. On Ramsey $(K_{1,2}, Kₙ)$-minimal graphs. Discussiones Mathematicae Graph Theory, Tome 32 (2012) pp. 331-339. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1604/
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