Minimalist designs
Combinatorics
2020-03-02 v3
Abstract
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.
Keywords
Cite
@article{arxiv.1808.06956,
title = {Minimalist designs},
author = {Ben Barber and Stefan Glock and Daniela Kühn and Allan Lo and Richard Montgomery and Deryk Osthus},
journal= {arXiv preprint arXiv:1808.06956},
year = {2020}
}
Comments
updated references, to appear in Random Structures & Algorithms