Fractional clique decompositions of partite graphs

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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, 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).

Details

Original languageEnglish
Pages (from-to)911-943
JournalCombinatorics, Probability and Computing
Volume26
Issue number6
Early online date19 Jun 2017
Publication statusPublished - Nov 2017