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Many disjoint triangles in co-triangle-free graphs
Published online by Cambridge University Press: 14 August 2020
Abstract
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.
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- © The Author(s), 2020. Published by Cambridge University Press