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The minimal density of triangles in tripartite graphs

Part of: Graph theory

Published online by Cambridge University Press:  01 August 2010

Rahil Baber ,
J. Robert Johnson  and
John Talbot
Rahil Baber
Affiliation:
Department of Mathematics, UCL, Gower Street, London WC1E 6BT, United Kingdom (email: rahilbaber@hotmail.com)
J. Robert Johnson
Affiliation:
School of Mathematical Sciences, Queen Mary University of London E1 4NS, United Kingdom (email: r.johnson@qmul.ac.uk)
John Talbot
Affiliation:
Department of Mathematics, UCL, Gower Street, London WC1E 6BT, United Kingdom (email: talbot@math.ucl.ac.uk)

Abstract

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We determine the minimal density of triangles in a tripartite graph with prescribed edge densities. This extends a previous result of Bondy, Shen, Thomassé and Thomassen characterizing those edge densities guaranteeing the existence of a triangle in a tripartite graph. To be precise we show that a suitably weighted copy of the graph formed by deleting a certain 9-cycle from K3,3,3 has minimal triangle density among all weighted tripartite graphs with prescribed edge densities.

Supplementary materials are available with this article.

MSC classification

Secondary: 05C35: Extremal problems
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 13 , January 2010 , pp. 388 - 413
Copyright
Copyright © London Mathematical Society 2010

References

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Supplementary material: File

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