论文标题
在无共同图的图中，许多分离三角形的三角形
Many disjoint triangles in co-triangle-free graphs
论文作者
论文摘要
我们证明，任何补语为三角形的$ n $ vertex图都包含$ n^2/12-o（n^2）$ edge-disshingoint Triangles。这对于两个订单$ n/2 $的差异结合而言是紧张的。我们还证明了相应的稳定性定理，所有达到上述结合的大图都接近两分。我们的结果回答了Alon和Linial的问题，并在Erds的猜想上取得了进展。
We prove that any $n$-vertex graph whose complement is triangle-free contains $n^2/12-o(n^2)$ 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.
