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When Hamilton circuits generate the cycle space of a random graph
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If eps > 0 and p >= n^{-1/2 + eps}, in a binomial random graph G(n,p) a.a.s. the set of cycles which can be constructed as a symmetric difference of Hamilton circuits is as large as parity by itself permits (all cycles if n is odd, all even cycles if n is even). Moreover, every p which ensures the above property a.a.s. must necessarily be such that for any constant c>0, eventually p >= (log n + 2 log log n + c)/n. So, whatever the smallest sufficient p for an a.a.s. Hamilton-generated cycle space might be, it does not coincide with the threshold for hamiltonicity of G(n,p).
Forward citations
Cited by 2 Pith papers
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On graphs whose cycle space is spanned by their Hamilton cycles
Under strengthened Chvátal-Erdős, McDiarmid-Yolov and dominating-set conditions with odd n, the cycle space equals the Hamilton-cycle subspace.
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The Hamilton cycle space of random regular graphs and randomly perturbed graphs
Hamilton cycles span the full cycle space asymptotically almost surely in random regular graphs of sufficiently large constant degree, and in randomly perturbed dense graphs.
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