Packing and counting arbitrary Hamilton cycles in random digraphs
نویسندگان
چکیده
We prove packing and counting theorems for arbitrarily oriented Hamilton cycles in D(n, p) for nearly optimal p (up to a logc n factor). In particular, we show that given t = (1 − o(1))np Hamilton cycles C1, . . . , Ct, each of which is oriented arbitrarily, a digraph D ∼ D(n, p) w.h.p. contains edge disjoint copies of C1, . . . , Ct, provided p = ω(log 3 n/n). We also show that given an arbitrarily oriented n-vertex cycle C, a random digraphD ∼ D(n, p) w.h.p. contains (1±o(1))n!p copies of C, provided p ≥ log n/n.
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