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Erdős-Hajnal-type Results on Intersection Patterns of Geometric Objects

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Horizons of Combinatorics

Part of the book series: Bolyai Society Mathematical Studies ((BSMS,volume 17))

Abstract

In their seminal paper [21], Erdős and Hajnal raised the following question. Is it true that for any graph G there exists a constant c = c(G) > 0 with the property that every graph of n vertices that contains no induced subgraph isomorphic to G has a complete or an empty induced subgraph of size n c? We answer this question in the affirmative for some special classes of graphs denned by geometric methods.

Supported by an NSF Graduate Research Fellowship and a Princeton Centennial Fellowship.

Supported by NSF Grant CCF-05-14079, and by grants from NSA, PSC-CUNY, the Hungarian Research Foundation OTKA, and BSF.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ, 08544-1000, USA

    Jacob Fox

  2. City College, CUNY and Courant Institute, NYU, 251 Mercer Street, New York, NY, 10012, USA

    János Pach

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  1. Jacob Fox
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  2. János Pach
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Editors and Affiliations

  1. Alfréd Rényi Inst. of Mathematics, Hungarian Academy of Sciences, Reáltanoda u. 13-15, Budapest, 1053, Hungary

    Ervin Győri , Gyula O. H. Katona  & Gábor Sági ,  & 

  2. Institute of Mathematics, Eötvös University, Pázmány Péter sétány 1/C, Budapest, 1117, Hungary

    László Lovász

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© 2008 János Bolyai Mathematical Society and Springer-Verlag

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Fox, J., Pach, J. (2008). Erdős-Hajnal-type Results on Intersection Patterns of Geometric Objects. In: Győri, E., Katona, G.O.H., Lovász, L., Sági, G. (eds) Horizons of Combinatorics. Bolyai Society Mathematical Studies, vol 17. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77200-2_4

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