Optimal Packings of Hamilton Cycles in Sparse Random Graphs

Michael Krivelevich, Wojciech Samotij

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Source: Crossref

Published: Jan 1, 2012

DOI: 10.1137/110849171

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Source abstract

We prove that there exists a positive constant $\varepsilon$ such that if $\log n / n \leq p \leq n^{-1+\varepsilon}$ , then asymptotically almost surely the random graph $G \sim G(n,p)$ contains a collection of $\lfloor \delta(G)/2 \rfloor$ edge-disjoint Hamilton cycles.

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Optimal Packings of Hamilton Cycles in Sparse Random Graphs — Mathematical Frontier Network