Large planar subgraphs in dense graphs

Authors:
Daniela Kühn;Deryk Osthus;Anusch Taraz
Affiliations:
School of Mathematics, Birmingham University, Edgbaston, Birmingham, UK;School of Mathematics, Birmingham University, Edgbaston, Birmingham, UK;Zentrum Mathematik, Technische Universität München, Garching bei München, Germany
Venue:
Journal of Combinatorial Theory Series B
Year:
2005

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Abstract

We prove sufficient and essentially necessary conditions in terms of the minimum degree for a graph to contain planar subgraphs with many edges. For example, for all positive γ every sufficiently large graph G with minimum degree at least (2/3+γ)|G| contains a triangulation as a spanning subgraph, whereas this need not be the case when the minimum degree is less than 2|G|/3.