无共三角形图中的许多不相交三角形

Combinatorics, Probability and Computing Pub Date : 2020-01-03 DOI:10.1017/S096354832000036X

Mykhaylo Tyomkyn

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引用次数: 1

摘要

摘要证明了补边无三角形的n顶点图包含n2/12 - o(n2)个边不相交三角形。这对于n/2阶的两个团的不相交并是紧的。我们还证明了一个相应的稳定性定理，即所有达到上述界的大图都接近于二部图。我们的结果回答了Alon和Linial的一个问题，并在Erdős的一个猜想上取得了进展。

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Many disjoint triangles in co-triangle-free graphs

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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Combinatorics, Probability and Computing

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