Fractional triangle decompositions of dense 3-partite graphs

2015/10/30 by Bowditch, Flora C., Dukes, Peter J. · 2 citations
#05B15 #05C70 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1510.08998

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.

Cited by

• On fractional triangle decompositions of random graphs
• Beyond Nash-Williams: Counterexamples to Clique Decomposition Thresholds for All Cliques Larger than Triangles

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• Progress towards Nash-Williams' Conjecture on Triangle Decompositions