Minimalist designs. Issue 1 (11th March 2020)

• Record Type: Journal Article
• Authors: Barber, Ben; Glock, Stefan; Kühn, Daniela; Lo, Allan; Montgomery, Richard; Osthus, Deryk
• Is Part Of: Random structures & algorithms. Volume 57:Issue 1(2020)
• Page Start: 47
• Page End: 63
• Publication Date: 2020-03-11
• Subjects: triangle decomposition -- iterative absorption -- extremal graph theory -- design theory; Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20915
• Languages: English
• ISSNs: 1042-9832

Abstract

Abstract : 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.