Fractional clique decompositions of partite graphs

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Fractional clique decompositions of partite graphs. / Montgomery, Richard.

In: Combinatorics, Probability and Computing, Vol. 26, No. 6, 11.2017, p. 911-943.

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@article{bae880699d44429ab1f21f80952c28e5,
title = "Fractional clique decompositions of partite graphs",
abstract = "We give a minimum degree condition sufficient to ensure the existence of a fractional Kr -decomposition in a balanced r-partite graph (subject to some further simple necessary conditions). This generalizes the non-partite problem studied recently by Barber, Lo, K{\"u}hn, Osthus and the author, and the 3-partite fractional K 3-decomposition problem studied recently by Bowditch and Dukes. Combining our result with recent work by Barber, K{\"u}hn, Lo, Osthus and Taylor, this gives a minimum degree condition sufficient to ensure the existence of a (non-fractional) Kr -decomposition in a balanced r-partite graph (subject to the same simple necessary conditions).",
author = "Richard Montgomery",
year = "2017",
month = nov,
doi = "10.1017/S0963548317000165",
language = "English",
volume = "26",
pages = "911--943",
journal = "Combinatorics, Probability and Computing",
issn = "0963-5483",
publisher = "Cambridge University Press",
number = "6",

}

RIS

TY - JOUR

T1 - Fractional clique decompositions of partite graphs

AU - Montgomery, Richard

PY - 2017/11

Y1 - 2017/11

N2 - We give a minimum degree condition sufficient to ensure the existence of a fractional Kr -decomposition in a balanced r-partite graph (subject to some further simple necessary conditions). This generalizes the non-partite problem studied recently by Barber, Lo, Kühn, Osthus and the author, and the 3-partite fractional K 3-decomposition problem studied recently by Bowditch and Dukes. Combining our result with recent work by Barber, Kühn, Lo, Osthus and Taylor, this gives a minimum degree condition sufficient to ensure the existence of a (non-fractional) Kr -decomposition in a balanced r-partite graph (subject to the same simple necessary conditions).

AB - We give a minimum degree condition sufficient to ensure the existence of a fractional Kr -decomposition in a balanced r-partite graph (subject to some further simple necessary conditions). This generalizes the non-partite problem studied recently by Barber, Lo, Kühn, Osthus and the author, and the 3-partite fractional K 3-decomposition problem studied recently by Bowditch and Dukes. Combining our result with recent work by Barber, Kühn, Lo, Osthus and Taylor, this gives a minimum degree condition sufficient to ensure the existence of a (non-fractional) Kr -decomposition in a balanced r-partite graph (subject to the same simple necessary conditions).

U2 - 10.1017/S0963548317000165

DO - 10.1017/S0963548317000165

M3 - Article

VL - 26

SP - 911

EP - 943

JO - Combinatorics, Probability and Computing

JF - Combinatorics, Probability and Computing

SN - 0963-5483

IS - 6

ER -