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Asymptotic Structure of Graphs with the Minimum Number of Triangles

Part of: Graph theory

Published online by Cambridge University Press:  04 May 2016

OLEG PIKHURKO  and
ALEXANDER RAZBOROV
OLEG PIKHURKO
Affiliation:
Mathematics Institute and DIMAP, University of Warwick, Coventry CV4 7AL, UK (e-mail: O.Pikhurko@warwick.ac.uk)
ALEXANDER RAZBOROV
Affiliation:
Department of Computer Science, University of Chicago, Chicago, IL 60637, USA (e-mail: razborov@cs.uchicago.edu)
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Abstract

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We consider the problem of minimizing the number of triangles in a graph of given order and size, and describe the asymptotic structure of extremal graphs. This is achieved by characterizing the set of flag algebra homomorphisms that minimize the triangle density.

MSC classification

Primary: 05C35: Extremal problems
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 26 , Issue 1 , January 2017 , pp. 138 - 160
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
Copyright © Cambridge University Press 2016

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