Journal of Combinatorics

Volume 10 (2019)

Number 2

Fractional triangle decompositions of dense $3$-partite graphs

Pages: 255 – 282

DOI: https://dx.doi.org/10.4310/JOC.2019.v10.n2.a5

Authors

Flora C. Bowditch (Department of Mathematics and Statistics, University of Victoria, British Columbia, Canada)

Peter J. Dukes (Department of Mathematics and Statistics, University of Victoria, British Columbia, Canada)

Abstract

We compute a minimum degree threshold sufficient for $3$-partite graphs to admit a fractional triangle decomposition. Together with recent work of Barber, Kühn, Lo, Osthus and Taylor, this leads to bounds for exact decompositions and in particular the completion problem for sparse partial latin squares. Some extensions are considered as well.

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The second author’s research is supported by NSERC grant 312595–2010.

Received 30 October 2015

Published 25 January 2019