Universal graphs with a forbidden subtree

• Autores: Gregory Cherlin, Saharon Shelah
• Localización: Journal of combinatorial theory. Series B, ISSN 0095-8956, Vol. 97, Nº. 3, 2007, págs. 293-333
• Idioma: inglés
• DOI: 10.1016/j.jctb.2006.05.008
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• Resumen

  • We show that the problem of the existence of universal graphs with specified forbidden subgraphs can be systematically reduced to certain critical cases by a simple pruning technique which simplifies the underlying structure of the forbidden graphs, viewed as trees of blocks. As an application, we characterize the trees T for which a universal countable T-free graph exists.