Proves that pancyclicity and Hamiltonicity thresholds coincide at ρ_r solving x^r + r x -1=0 for graphs perturbed by a uniform random K_r-factor.
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3 Pith papers cite this work. Polarity classification is still indexing.
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math.CO 3years
2026 3verdicts
UNVERDICTED 3representative citing papers
The sharp threshold for Hamiltonicity in G_α ∪ G(n,p) is p = (1+o(1)) log(1/α)/n when αn → ∞.
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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Pancyclicity of graphs perturbed by a random $F$-factor
Proves that pancyclicity and Hamiltonicity thresholds coincide at ρ_r solving x^r + r x -1=0 for graphs perturbed by a uniform random K_r-factor.
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Sharp threshold for Hamilton cycles in randomly perturbed sparse graphs
The sharp threshold for Hamiltonicity in G_α ∪ G(n,p) is p = (1+o(1)) log(1/α)/n when αn → ∞.
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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.