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    題名: Decomposing Kn ∪ P into triangles
    作者: 高金美;Kau, Chin-mei;Fu, Hung-lin;Rodger, C. A.
    貢獻者: 淡江大學數學學系
    關鍵詞: Triple system;Covering;Forest
    日期: 2004-06-06
    上傳時間: 2010-01-28 06:59:41 (UTC+8)
    出版者: Elsevier
    摘要: In this paper, we extend the work on minimum coverings of Kn with triangles. We prove that when P is any forest on n vertices the multigraph G=Kn∪P can be decomposed into triangles if and only if three trivial necessary conditions are satisfied: (i) each vertex in G has even degree, (ii) each vertex in P has odd degree, and (iii) the number of edges in G is a multiple of 3. This result is of particular interest because the corresponding packing problem where the leave is any forest is yet to be solved. We also consider some other families of packings, and provide a variation on a proof by Colbourn and Rosa which settled the packing problem when P is any 2-regular graph on at most n vertices.
    關聯: Discrete Mathematics 284(1-3), pp.131-136
    DOI: 10.1016/j.disc.2003.04.003
    顯示於類別:[數學學系暨研究所] 期刊論文


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