The complete multigraph lambdaKnu is said to have a G-decomposition if it is the union of edge disjoint subgraphs of K-nu each of them isomorphic to a fixed graph G. The spectrum problem for G-decompositions of K, that have a nesting was first considered in the case G=K-3 by Colbourn and Colbourn (Ars Combin. 16 (1983) 27-34) and Stinson (Graphs and Combin. 1 (1985) 189 -191). For lambda=1 and G=C-m (the cycle of length m) this problem was studied in many papers, see Lindner and Rodger (in: J.H. Dinitz, D.R. Stinson (Eds.), Contemporary Design Theory: A Collection of Surveys, Wiley, New York, 1992, p. 325-369), Lindner et al. (Discrete Math. 77 (1989) 191-203), Lindner and Stinson (J. Combin. Math. Combin. Comput. 8 (1990) 147-157) for more details and references. For lambda=1 and G=P-k (the path of length k - 1) the analogous problem was considered in Milici and Quattrocchi (J. Combin. Math. Combin. Comput. 32 (2000) 115-127). In this paper we solve the spectrum problem of nested G-decompositions of lambdaK(nu) for all the graphs G having four nonisolated vertices or less, leaving eight possible exceptions. (C) 2002 Elsevier Science B.V. All rights reserved.

On nesting of G-decompositions of lambda K-v where G has four nonisolated vertices or less

MILICI, Salvatore;
2002

Abstract

The complete multigraph lambdaKnu is said to have a G-decomposition if it is the union of edge disjoint subgraphs of K-nu each of them isomorphic to a fixed graph G. The spectrum problem for G-decompositions of K, that have a nesting was first considered in the case G=K-3 by Colbourn and Colbourn (Ars Combin. 16 (1983) 27-34) and Stinson (Graphs and Combin. 1 (1985) 189 -191). For lambda=1 and G=C-m (the cycle of length m) this problem was studied in many papers, see Lindner and Rodger (in: J.H. Dinitz, D.R. Stinson (Eds.), Contemporary Design Theory: A Collection of Surveys, Wiley, New York, 1992, p. 325-369), Lindner et al. (Discrete Math. 77 (1989) 191-203), Lindner and Stinson (J. Combin. Math. Combin. Comput. 8 (1990) 147-157) for more details and references. For lambda=1 and G=P-k (the path of length k - 1) the analogous problem was considered in Milici and Quattrocchi (J. Combin. Math. Combin. Comput. 32 (2000) 115-127). In this paper we solve the spectrum problem of nested G-decompositions of lambdaK(nu) for all the graphs G having four nonisolated vertices or less, leaving eight possible exceptions. (C) 2002 Elsevier Science B.V. All rights reserved.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/46883
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