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asymptotic beliebige belong Beweis BIBD classes Combinatorial common edges complete graph complete subgraph conjugacy classes connected consider construction cycle of order define denote the number Eigenwert endpoints enthalten ERDOS exists extremal graph finite graphs fixed cycle folgt gibt gilt graph G graph theory Graphen G Hamilton-cycles Hamiltonian Hamiltonian circuits hyperplane incident infinite integer interior positions joined k-tree k-tuple Kanten Knotenpunkte Kreise labelled Lemma log log Logn Math matrix minimal number of cycles number of edges numbers 1,2 obtained omitted edges original cycle ot(G partitions permutation plane of order point-independent possible primitive Prufer problem projective plane proof of Theorem prove Prufer codeword Ramsey's theorem representative system Room Squares rooted tree Satz Selberg sieve sequence Square of side Steiner triple systems subset subtree summands theory total number tree of order triangles Tripel triplets tuples valency vertex vertices weak element Zahl zwei