Hamiltonicity of Random Subgraphs of the Hypercube: 1534 - Brossura

Condon, Padraig; Diaz, Alberto Espuny; Girao, Antonio; Kuhn, Daniela; Osthus, Deryk

Brossura

ISBN 10: 147047266X ISBN 13: 9781470472665

Casa editrice: Amer Mathematical Society, 2025

Riassunto

"We study Hamiltonicity in random subgraphs of the hypercube Qn. Our first main theorem is an optimal hitting time result. Consider the random process which includes the edges of Qn according to a uniformly chosen random ordering. Then, with high probability, as soon as the graph produced by this process has minimum degree 2k, it contains k edge-disjoint Hamilton cycles, for any fixed k N. Secondly, we obtain a perturbation result: if H Qn satisfies (H) n with 0 fixed and we consider a random binomial subgraph Qnp of Qn with p (0, 1] fixed, then with high probability HQnp contains k edge-disjoint Hamilton cycles, for any fixed k N. In particular, both results resolve a long standing conjecture, posed e.g. by Bollobas, that the threshold probability for Hamiltonicity in the random binomial subgraph of the hypercube equals 1/2. Our techniques also show that, with high probability, for all fixed p (0, 1] the graph Qnp contains an almost spanning cycle. Our methods involve branching processes, the Rodl nibble, and absorption"-- Provided by publisher.

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Informazioni sull?autore

Padraig Condon, University of Birmingham, United Kingdom, Alberto Espuny Diaz, University of Birmingham, United Kingdom, Antonio Girao, University of Birmingham, United Kingdom, Daniela Kuhn, University of Birmingham, United Kingdom, and Deryk Osthus, University of Birmingham, United Kingdom

Dettagli dell'edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 2025
• Lingua: Inglese
• ISBN 10: 147047266X
• ISBN 13: 9781470472665
• Rilegatura: Copertina flessibile
• Numero di pagine: 132
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile