The iterative absorption method has recently led to major progress in the area of (hyper‐)graph decompositions. Among other results, a new proof of the existence conjecture for combinatorial designs, and some generalizations, was obtained. Here, we illustrate the method by investigating triangle decompositions: We give a simple proof that a triangle‐divisible graph of large minimum degree has a triangle decomposition and prove a similar result for quasi‐random host graphs.

中文翻译：

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极简设计

迭代吸收法最近在（超）图分解领域取得了重大进展。在其他结果中，获得了组合设计存在猜想的新证明以及一些概括。在这里，我们通过研究三角分解来说明该方法：我们给出一个简单的证明，即最小最小度的三角可分解图具有三角分解，并证明了拟随机主体图的相似结果。