In this paper we translate Ramsey-type problems into the language of decomposable hereditary properties of graphs. We prove a distributive law for reducible and decomposable properties of graphs. Using it we establish some values of graph theoretical invariants of decomposable properties and show their correspondence to generalized Ramsey numbers.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1095, author = {Stefan A. Burr and Michael S. Jacobson and Peter Mih\'ok and Gabriel Semani\v sin}, title = {Generalized ramsey theory and decomposable properties of graphs}, journal = {Discussiones Mathematicae Graph Theory}, volume = {19}, year = {1999}, pages = {199-217}, zbl = {0958.05094}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1095} }
Stefan A. Burr; Michael S. Jacobson; Peter Mihók; Gabriel Semanišin. Generalized ramsey theory and decomposable properties of graphs. Discussiones Mathematicae Graph Theory, Tome 19 (1999) pp. 199-217. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1095/
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