Spanning cycles in random directed graphs

Abstract

AbstractWe show that, in almost every ‐vertex random directed graph process, a copy of every possible ‐vertex oriented cycle will appear strictly before a directed Hamilton cycle does, except of course for the directed cycle itself. Furthermore, given an arbitrary ‐vertex oriented cycle, we determine the sharp threshold for its appearance in the binomial random directed graph. These results confirm, in a strong form, a conjecture of Ferber and Long.