English

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

R2 v1 2026-06-23T03:39:38.543Z