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A Density Corrádi–Hajnal Theorem

Published online by Cambridge University Press:  20 November 2018

Peter Allen ,
Julia Böttcher ,
Jan Hladký  and
Diana Piguet
Peter Allen
Affiliation:
Department of Mathematics, London School of Economics, Houghton Street, London, WC2A 2AE, UK e-mail: [email protected], [email protected]
Julia Böttcher
Affiliation:
Department of Mathematics, London School of Economics, Houghton Street, London, WC2A 2AE, UK e-mail: [email protected], [email protected]
Jan Hladký
Affiliation:
Institute of Mathematics of the Czech Academy of Sciences of the Czech Republic, Žitná 25, Praha, Czech Republic, The Institute of Mathematics is supported by RVO:67985840 e-mail: [email protected]
Diana Piguet
Affiliation:
New Technologies for Information Society, University of West Bohemia, Pilsen, Czech Republic e-mail: [email protected]
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Abstract

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We find, for all sufficiently large $n$ and each $k$, the maximum number of edges in an $n$-vertex graph that does not contain $k\,+\,1$ vertex-disjoint triangles.

This extends a result of Moon [Canad. J. Math. 20 (1968), 96–102], which is in turn an extension of Mantel's Theorem. Our result can also be viewed as a density version of the Corrádi–Hajnal Theorem.

Keywords

05C35graph theoryTuran's TheoremMantel's TheoremCorrádi–Hajnal Theoremtriangle
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 67 , Issue 4 , 01 August 2015 , pp. 721 - 758
Copyright
Copyright © Canadian Mathematical Society 2015

References

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