Many disjoint triangles in co-triangle-free graphs

Mykhaylo Tyomkyn*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 Erdos.

Original languageEnglish
Pages (from-to)153-162
Number of pages10
JournalCombinatorics Probability and Computing
Issue number1
StatePublished - Jan 2021
Externally publishedYes


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