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摘要
In this paper, two related problems are completely solved, extending two classic results by Colbourn and Rosa. In any partial triple system (V, B) of 2K(n), the neighborhood of a vertex v is the subgraph induced by {{x, y} vertical bar {v, x, y}. B}. For n = 2 (mod 3) with n not equal 2, it is shown that for any 2-factor F on n -1 or n -2 vertices, there exists amaximum packing of 2K(n) with triples such that F is the neighborhood of some vertex if and only if (n, F) not equal (5, C-2 boolean OR C-2), thus extending the corresponding result for the case where n = 0 or 1 (mod 3) by Colbourn and Rosa. This result, along with the companion result of Colbourn and Rosa, leads to a complete characterization of quadratic leaves of.-fold partial triple systems for all lambda %26gt;= 2, thereby extending the solution where lambda = 1 by Colbourn and Rosa.
- 出版日期2014-12
