English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study the existence of a directed Hamilton cycle in random digraphs with$m$ edges where we condition on minimum in- and out-degree at least one. Denotesuch a random graph by $D_{n,m}^{(\delta\geq1)}$. We prove that if $m=\tfracn2(\log n+2\log\log n+c_n)$ then \[\lim_{n\to\infty}\Pr(D_{n,m}^{(\delta\geq1)}\text{ isHamiltonian})=\begin{cases}0&c_n\to-\infty.\\e^{-e^{-c}/4}&c_n\toc.\\1&c_n\to\infty.\end{cases} \]

Hamilton cycles in random digraphs with minimum degree at least one