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Many disjoint triangles in co-triangle-free graphs

Part of: Graph theory

Published online by Cambridge University Press:  14 August 2020

Mykhaylo Tyomkyn
Mykhaylo Tyomkyn*
Affiliation:
Department of Mathematics, California Institute of Technology, Pasadena, CA 91125, USA
*
Email: tyomkyn@caltech.edu
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Abstract

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We prove that any n-vertex graph whose complement is triangle-free contains n2/12 – o(n2) edge-disjoint triangles. This is tight for the disjoint union of two cliques of order n/2. We also prove a corresponding stability theorem, that all large graphs attaining the above bound are close to being bipartite. Our results answer a question of Alon and Linial, and make progress on a conjecture of Erdős.

MSC classification

Primary: 05C35: Extremal problems
Secondary: 05C70: Factorization, matching, partitioning, covering and packing

Information

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 30 , Issue 1 , January 2021 , pp. 153 - 162
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

References

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