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1-factorization adjacent arêtes assume BIBD block intersection graph chaînes colour columns Combinatorial complete graph conjecture conjugate invariant subgroup consider construction contained contradiction crossing-free cubic graph cycle define denote diameter dominating set edges elements embedded exactly exists finite fleur graph G graph of type Graph Theory Hamiltonian path Hamming Codes Hence hypergraph implies initial blocks integer intersection graph isomorphic Latin rectangle Lemma Let G linear code longueur Lw(l Math Mathematics matrix Mendelsohn minimal change n-critical n-tuple nesting nodes nombre non-zero entries obtained order q parameters path in G(P perfect competition permutation perpendicular arrays positive integers prove the following quasi-multiple design r-partitioned graph Rao designs realisable repeated pair result rinds rows Seberry sequence set-system signed over Z2 solution sommets special subgraph Steiner triple system STS(v Subcase subsets Suppose Theorem tion type K(n vertex vertices of G