| PACKINGS OF THE COMPLETE DIRECTED GRAPH WITH m-CIRCUITS |
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| 作者姓名： | LIANGZHIHE KANGQINGDE |
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| 作者单位： | DepartmentofMathematlcs,HebeiNormalUniversity,Shijiazhuang050091 |
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| 摘 要： | A packing of the complete directed symmetric graph DKv with m-circuits, denoted by(v,m)-DCP, is defined to he a family of are-disjoint m-circuits of DK, such that any one arc of DKv occurs in at most one m circuit. The packing number P(v,m) is the maximum number of m-circults in such a packing. The packing problem is to determine the value P(v,m) for everyinteger v ≥ m. In this paper, the problem is reduced to the case m 6 ≤v≤2m-(4m-3的平方极) 1/2]，for any fixed even integer m≥4，In particular,the values of P（v,m） are completely determined for m=12,14 and 16.
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| 关 键 词： | 完全直接图 存储问题 m-路径 对称图 |
| 收稿时间： | 22 September 1997 |
Packings of the complete directed graph with m-circuits |
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| LIANGZHIHE KANGQINGDE.PACKINGS OF THE COMPLETE DIRECTED GRAPH WITH m-CIRCUITS[J].Applied Mathematics A Journal of Chinese Universities,1998,13(4):463-472. |
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| Authors: | Liang Zhihe Kang Qingde |
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| Institution: | (1) Department of Mathematics, Hebei Normal University, 050091 Shijiazhuang |
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| Abstract: | A packing of the complete directed symmetric graph DKv with m-circuits, denoted by (v,m)-DCP, is defined to be a family of arc-disjoint m-circuits of DKv such that any one arc of DKv occurs in at most one m-circuit. The packing number P(v,m) is the maximum number of m-circuits in such a packing. The packing problem is to determine the value P(v,m) for every integer v ≥ m. In this paper, the problem is reduced to the case
![$$m + 6 \leqslant \upsilon \leqslant 2m{\text{ - }}\left {\frac{{\sqrt {{\text{4}}m - 3 + 1} }}{2}} \right]$$](/content/lt3516445200g158/11766_1998_Article_60_TeX2GIFIE1.gif)
for any fixed even integer m≥4. In particular, the values of P(v,m) are completely determined for m = 12, 14 and 16.
Research supported by HNSF (197173). |
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| Keywords: | Complete directed graph m-circuit packing packing number |
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