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Fractional Clique Decompositions of Dense Partite Graphs

Part of: Graph theory

Published online by Cambridge University Press:  19 June 2017

RICHARD MONTGOMERY
RICHARD MONTGOMERY*
Affiliation:
Trinity College, Cambridge CB2 1TQ, UK (e-mail: rhm34@cam.ac.uk)
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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 K3-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).

MSC classification

Primary: 05C51: Graph designs and isomomorphic decomposition
Secondary: 05C72: Fractional graph theory, fuzzy graph theory
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 26 , Issue 6 , November 2017 , pp. 911 - 943
Copyright
Copyright © Cambridge University Press 2017 

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References

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