Minimalist designs

Ben Barber; Stefan Glock; Daniela Kühn; Allan Lo; Richard Montgomery; Deryk Osthus

Minimalist designs

Ben Barber
, Stefan Glock
, Daniela Kühn
, Allan Lo
, Richard Montgomery
, Deryk Osthus

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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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.

Original language	English
Journal	arXiv
Publication status	Submitted - 21 Aug 2018

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title = "Minimalist designs",

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. ",

author = "Ben Barber and Stefan Glock and Daniela K{\"u}hn and Allan Lo and Richard Montgomery and Deryk Osthus",

year = "2018",

month = aug,

day = "21",

language = "English",

journal = "arXiv",

publisher = "Cornell University",

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TY - JOUR

T1 - Minimalist designs

AU - Barber, Ben

AU - Glock, Stefan

AU - Kühn, Daniela

AU - Lo, Allan

AU - Montgomery, Richard

AU - Osthus, Deryk

PY - 2018/8/21

Y1 - 2018/8/21

N2 - 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.

AB - 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.

UR - http://arxiv.org/abs/1808.06956v1

M3 - Article (Academic Journal)

JO - arXiv

JF - arXiv

ER -

Minimalist designs

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