Hamiltonicity of Random Subgraphs of the Hypercube (Memoirs of the American Mathematical Society, 304) - Softcover

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

 
9781470472665: Hamiltonicity of Random Subgraphs of the Hypercube (Memoirs of the American Mathematical Society, 304)
Softcover
ISBN 10: 147047266X ISBN 13: 9781470472665
Verlag: American Mathematical Society, 2025

Inhaltsangabe

"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.

Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.

Über die Autorin bzw. den Autor

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

„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
American Mathematical Society
Erscheinungsdatum
2025
Sprache
Englisch
ISBN 10 
147047266X
ISBN 13 
9781470472665
Einband
Taschenbuch
Anzahl der Seiten
132
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
Buchbär
info@buchbaer.de

Weberstr. 67
Osnabrück
49084
Deutschland