University of Birmingham > Talks@bham > Combinatorics and Probability seminar > Spanning cycles in random directed graphs.

Spanning cycles in random directed graphs.

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If you have a question about this talk, please contact Johannes Carmesin.

A beautiful coupling argument of McDiarmid shows that, given any orientated n-vertex cycle C, a copy of C almost surely appears in D(n,p) if p=(log n+log log n+omega(1))/n. This is not always optimal—as Frieze had shown, for a directed Hamilton cycle p=(log n+omega(1))/n is sufficient.

This talk will address the following questions, by combining McDiarmid’s coupling with constructive techniques:

- Is p=(log n+omega(1))/n sufficient for the appearance of any oriented n-vertex cycle?

- When is it likely that a copy of all such cycles can be found simultaneously?

This talk is part of the Combinatorics and Probability seminar series.

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