The authors prove that every triangle-divisible graph on n vertices with minimum degree at least (3/4)n has a triangle decomposition for large n.
Beyond Nash–Williams: Counterexamples to clique decomposition thresholds for all cliques larger than triangles
3 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
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math.CO 3years
2026 3verdicts
UNVERDICTED 3representative citing papers
For dn-regular G_d union G(n,p) with p > 2d/(1+2d), there is whp a triangle packing covering all but o(n²) edges, and the bound is sharp for d ≤ 1/2.
New explicit degree thresholds are established for fractional K_s-decompositions of balanced multipartite graphs when the number of parts exceeds the clique size.
citing papers explorer
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A Proof of Nash-Williams' Conjecture
The authors prove that every triangle-divisible graph on n vertices with minimum degree at least (3/4)n has a triangle decomposition for large n.
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Triangle packings in randomly perturbed graphs
For dn-regular G_d union G(n,p) with p > 2d/(1+2d), there is whp a triangle packing covering all but o(n²) edges, and the bound is sharp for d ≤ 1/2.
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Fractional clique decompositions of dense balanced multipartite graphs
New explicit degree thresholds are established for fractional K_s-decompositions of balanced multipartite graphs when the number of parts exceeds the clique size.