Orthogonal H-decompositions
نویسندگان
چکیده
An H-decomposition of a graph G is a set L of edge-disjoint Hsubgraphs of G, such that each edge of G appears in some element of L. A k-orthogonal H-decomposition of a graph G is a set of k H-decompositions of G, such that any two copies of H in any two distinct H-decompositions have at most one edge in common. We prove that for every fixed graph H and every fixed integer k ≥ 1, if n is sufficiently large then Kn has a k-orthogonal H decomposition if and only if it has an H-decomposition. This occurs whenever ( n 2 ) is a multiple of e(H) and n− 1 is a multiple of the gcd of the degrees of H.
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