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
Hauptverfasser: Barber, Ben, Glock, Stefan, Kühn, Daniela, Lo, Allan, Montgomery, Richard, Osthus, Deryk
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container_end_page 63
container_issue 1
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container_title Random structures & algorithms
container_volume 57
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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source Wiley Online Library Journals Frontfile Complete
subjects Combinatorial analysis
Decomposition
Design theory
extremal graph theory
iterative absorption
triangle decomposition
title Minimalist designs
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