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The exact minimum number of triangles in graphs with given order and size

Abstract:

What is the minimum number of triangles in a graph of given order and size? Motivated by earlier results of Mantel and Turán, Rademacher solved the first nontrivial case of this problem in 1941. The problem was revived by Erdős in 1955; it is now known as the Erdős–Rademacher problem. After attracting much attention, it was solved asymptotically in a major breakthrough by Razborov in 2008. In this paper, we provide an exact solution for all large graphs whose edge density is bounded away from...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1017/fmp.2020.7

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
ORCID:
0000-0002-9968-9148
Publisher:
Cambridge University Press Publisher's website
Journal:
Forum of Mathematics, Pi Journal website
Volume:
8
Article number:
e8
Publication date:
2020-04-20
Acceptance date:
2020-03-04
DOI:
EISSN:
2050-5086
Language:
English
Keywords:
Pubs id:
820650
Local pid:
pubs:820650
Deposit date:
2020-04-24

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