Gaetano Quattrocchi

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Let D be the triangle with an attached edge (i. e. D is the “kite”, a graph having vertices {a0, a1, a2, a3} and edges {a0, a1}, {a0, a2}, {a1, a2}, {a0, a3}). Bermond and Schönheim [6] proved that a kite-design of order n exists if and only if n ≡ 0 or 1 (mod 8). Let (W, C) be a nontrivial kite-design of order n ≥ 8, and let V ⊂ W with |V | = v < n. A path(More)
Let (W, C) be an m-cycle system of order n and let Ω ⊂ W , |Ω| = v < n. We say that a path design (Ω,P) of order v and block size s (2 ≤ s ≤ m− 1) is embedded in (W, C) if for every p ∈ P there is an m-cycle c = (a1, a2, . . . , am) ∈ C such that: (1) p = [ak, ak+1, . . . , ak+s−1] for some k ∈ {1, 2, . . . ,m} (i.e. the (s− 1)-path p occurs in the m-cycle(More)
Let (W;C) be an m-cycle system of order n and let ⊂W , | | = v¡n. We say that a handcu ed design ( ;P) of order v and block size s (26s6m − 1) is contained in (W;C) if for every p ∈ P there is an m-cycle c=(a1; a2; : : : ; am) ∈ C such that: (1) p=[ak ; ak+1; : : : ; ak+s−1] for some k ∈ {1; 2; : : : ; m} (i.e. the (s−1)-path p occurs in the m-cycle c); and(More)
Minimizing the number of add-drop multiplexers (ADMs) in a unidirectional SONET ring can be formulated as a graph decomposition problem. When traffic requirements are uniform and all-to-all, groomings that minimize the number of ADMs (equivalently, the drop cost) have been characterized for grooming ratio at most six. However, when two different traffic(More)
In a problem arising in grooming for two-period optical networks, it is required to decompose the complete graph on n vertices into subgraphs each containing at most C edges, so that the induced subgraphs on a specified set of v ≤ n vertices each contain at most C ′ < C edges. The cost of the grooming is the sum, over all subgraphs, of the number of(More)
A 5-cycle system on v + w points embeds a balanced P4-design on v points if there is a subset of v points on which the 5-cycles induce the blocks of a balanced P4-design. The mininum possible such w is: v (mod 30) w v ≡ 4, 16 v−1 3 v ≡ 7, 10, 22, 25 v+5 3 v ≡ 1, 13, 28 v+11 3 v ≡ 19 (mod 30) v+17 3 We shall show this minimum value of w is attained. AMS(More)
Let D be the triangle with attached edge (i. e. D is the graph having vertices {a0, a1, a2, a3} and edges {a0, a1}, {a0, a2}, {a1, a2}, {a0, a3}). J.C. Bermond and J. Schönheim [1], proved that a D-design of order n exists if and only if n ≡ 0 or 1 (mod 8). Let (W, C) be a nontrivial D-design of order n, n ≥ 8, and let V ⊂ W , |V | = v < n. We say that a(More)