Counting orientations of random graphs with no directed k‐cycles

For every k⩾3$$ k\geqslant 3 $$, we determine the order of growth, up to polylogarithmic factors, of the number of orientations of the binomial random graph containing no directed cycle of length k$$ k $$. This solves a conjecture of Kohayakawa, Morris and the last two authors.

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Bibliographic Details
Published in:	Random structures & algorithms Vol. 64; no. 3; pp. 676 - 691
Main Authors:	Campos, Marcelo, Collares, Maurício, Mota, Guilherme Oliveira
Format:	Journal Article
Language:	English
Published:	New York John Wiley & Sons, Inc 01-05-2024 Wiley Subscription Services, Inc
Subjects:	directed cycles orientations random graphs
Online Access:	Get full text
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Description
Summary:	For every k⩾3$$ k\geqslant 3 $$, we determine the order of growth, up to polylogarithmic factors, of the number of orientations of the binomial random graph containing no directed cycle of length k$$ k $$. This solves a conjecture of Kohayakawa, Morris and the last two authors.
ISSN:	1042-9832 1098-2418
DOI:	10.1002/rsa.21196