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Hypercycles in a random hypergraph. (Russian) Zbl 0745.05036
Let $$G$$ be a hypergraph. The authors define a hypercycle of $$G$$ to be a set $$A$$ of edges of $$G$$ such that each vertex of $$G$$ is incident with an even number of edges in $$A$$. Let $$S(G)=2^{s(G)}-1$$, where $$s(G)$$ is the maximum number of independent cycles in $$G$$. It is shown that for $$r$$- regular random hypergraph with $$n$$ vertices and $$t$$ edges, each edge having at most $$r$$ vertices, $$n,t\to\infty$$, $${n\over t}\to\alpha$$ there exists a constant $$\alpha_ r$$ such that $$MS(G)\to 0$$ for $$\alpha < \alpha_ r$$ and $$MS(G)\to\infty$$ for $$\alpha > \alpha_ r$$.

##### MSC:
 05C65 Hypergraphs 05C38 Paths and cycles
##### Keywords:
hypercycles; random hypergraph