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Title: Packing and counting arbitrary Hamilton cycles in random digraphs

We prove packing and counting theorems for arbitrarily oriented Hamilton cycles in(n, p) for nearly optimalp(up to afactor). In particular, we show that givent = (1 − o(1))npHamilton cyclesC1,…,Ct, each of which is oriented arbitrarily, a digraph(n, p) w.h.p. contains edge disjoint copies ofC1,…,Ct, provided. We also show that given an arbitrarily orientedn‐vertex cycleC, a random digraph(n, p) w.h.p. contains (1 ± o(1))n!pncopies ofC, provided.

 
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NSF-PAR ID:
10074761
Author(s) / Creator(s):
 ;  
Publisher / Repository:
Wiley Blackwell (John Wiley & Sons)
Date Published:
Journal Name:
Random Structures & Algorithms
Volume:
54
Issue:
3
ISSN:
1042-9832
Page Range / eLocation ID:
p. 499-514
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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