Minimalist designs

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Colleges, School and Institutes


The iterative absorption method has recently led to major progress in the area of (hyper-)graph decompositions. Amongst 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.


Original languageEnglish
JournalRandom Structures and Algorithms
Publication statusPublished - 2020