Minimalist designs
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 dec...
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Veröffentlicht in: | Random structures & algorithms 2020-08, Vol.57 (1), p.47-63 |
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creator | Barber, Ben Glock, Stefan Kühn, Daniela Lo, Allan Montgomery, Richard Osthus, Deryk |
description | 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. |
doi_str_mv | 10.1002/rsa.20915 |
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subjects | Combinatorial analysis Decomposition Design theory extremal graph theory iterative absorption triangle decomposition |
title | Minimalist designs |
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