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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
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