Geodesic
On the compatibility of a system of random comparisons
Diskretnaya Matematika, Tome 4 (1992) no. 3, pp. 75-85 
V. F. Kolchin. On the compatibility of a system of random comparisons. Diskretnaya Matematika, Tome 4 (1992) no. 3, pp. 75-85. http://geodesic.mathdoc.fr/item/DM_1992_4_3_a5/
@article{DM_1992_4_3_a5,
     author = {V. F. Kolchin},
     title = {On the compatibility of a~system of random comparisons},
     journal = {Diskretnaya Matematika},
     pages = {75--85},
     year = {1992},
     volume = {4},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1992_4_3_a5/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a random graph whose each cycle is marked with a certain probability depending on the cycle length. The asymptotic behaviour of the probability of absence of non-marked cycles is described. As a corollary, the asymptotic behaviour of the probability of consistency of a system of random congruences modulo two with random non-equiprobable right-hand sides and also of a system with non-random right-hand sides is described.