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完全二部图的P_(4k-1)-因子分解 被引量：3

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摘要 如果完全二部图Km,n的边集可以划分为Km,n的Pv-因子,则称Km,n存在Pv-因子分解.当v是偶数时,Ushio和Wang给出了Km,n存在Pv-因子分解的充分必要条件.Ushio同时提出了当v是奇数时Km,n存在Pv-因子分解的猜想,但是至今为止仅知当v=3时Ushio猜想成立.对于正整数k,本文证明Km,n存在P4k-1-因子分解的充分必要条件是:(1)(2k-1)m≤2kn,(2)(2k-1)n≤2km,(3)m+n=0(mod4k-1),(4)(4k-1)mn/[2(2k-1)(m+n)]是整数.即证明了对于任意正整数k,当v=4k-1时Ushio猜想成立.
作者 杜北梁 王建
机构地区 苏州大学数学科学学院 南通职业大学
出处 《中国科学（A辑）》 CSCD 北大核心 2005年第2期206-215,共10页 Science in China(Series A)
基金 国家自然科学基金资助项目(批准号:10071056)
关键词 P4k-1-因子分解 完全二部图 Ushio猜想 素数
分类号 O157.5 [理学—基础数学]
  • 相关文献

参考文献12

  • 1杜北梁,王建.完全二部图K_(m,n)的K_(p,q)-因子分解[J].中国科学（A辑）,2004,34(2):237-242. 被引量：2
  • 2Ushio K. G-designs and related designs. Discrete Math, 1993, 116:299-311.
  • 3Bondy J A, Murty U S R. Graph Theory with Applications. London: MacMillan Press, 1976.
  • 4Yamamoto S, lkeda H, Shige-eda S, et al. Design of a new balanced file organization scheme with the least redundancy. Information and Control, 1975, 28:156-175.
  • 5Yamamoto S, Tazawa S, Ushio K, et al. Design of a generalized balanced multiple-valued file organization scheme with the least redundancy. ACM Trans Database Systems, 1979, 4:518-530.
  • 6Ushio K.P3-factorization of complete bipartite graphs. Discrete Math, 1988, 72:361-366.
  • 7Martin N. Complete bipartite factorisations by complete bipartite graphs. Discrete Math, 1997, 167-168:461-480.
  • 8Du B L. K1,p^2 -factorization of complete bipartite graphs. Discrete Math, 1998, 187:273-279.
  • 9Du B L, Wang J. K1,k-factorizations of complete bipartite graphs. Discrete Math, 2002, 259:301-306.
  • 10Wang H. P2k-factorization of a complete bipartite graph. Discrete Math, 1993, 120:307-308.

二级参考文献9

  • 1Ushio K. G-designs and related designs. Discrete Math, 1993, 116:299-311
  • 2Bondy J A, Murty U S R. Graph Theory with Applications. London: Macmillan Press, 1976
  • 3Yamamoto S, Tazawa S, Ushio K, et al. Design of a balanced multiple-valued file organization scheme with the least redundancy. ACM Trans Database Systems, 1979, 4:518-530
  • 4Ushio K. P3-factorization of complete bipartite graphs. Discrete Math, 1988,72:361-366
  • 5Wang H. On K1,k-factorizations of a complete bipartite graph. Discrete Math, 1994, 126:359-364
  • 6Du B L. K1,p2-factorization of complete bipartite graphs. Discrete Math, 1998, 187:273-279
  • 7Du B L. K1,pq-factorization of complete bipartite graphs. Austral J Combin, 2002, 26:85-92
  • 8Du B L, Wang J. K1,k-factorizations of complete bipartite graphs. Discrete Math, 2002, 259:301-306
  • 9Martin N. Complete bipartite factorisations by complete bipartite graphs. Discrete Math, 1997, 167/168:461-480

共引文献1

同被引文献27

  • 1杜北梁,王建.完全二部图存在路因子分解的Ushio猜想的证明[J].中国科学（A辑）,2006,36(1):109-120. 被引量：2
  • 2王建,杜北梁.二部多重图的P_(4k-1)-因子分解[J].中国科学（A辑）,2006,36(8):928-937. 被引量：1
  • 3Ushio K. G-designs and related designs. Discrete Math, 1993, 116:299-311.
  • 4Bondy J A, Murty U S R. Graph Theory with Applications. London: Macmillan Press, 1976.
  • 5Yamamoto S, Ikeda H, Shige-eda S, et al. Design of a new balanced file organization scheme with the least redundancy, information and Control. 1975.28:156-175.
  • 6Yamamoto S, Tazawa S, Ushio K, et al. Design of a generalized balanced multiple-valued file organization scheme with the least redundancy. ACM Trans Database Systems, 1979, 4:518-530.
  • 7Ushio K, P3 factorization of complete bipartite graphs. Discrete Math, 1988, 72; 361-366.
  • 8Martin N. Complete bipartite factorisations by complete bipartite graphs. Discrete Math, 1997, 167 168:461 -480.
  • 9Du B L. K1,p^2-factorization of complete bipartite graphs, Discrete Math, 1998, 187:273-279.
  • 10Du B L, Wang J. K1,k-factorizations of complete bipartite graphs, Discrete Math, 2002, 259:301-306.

引证文献3

二级引证文献2

中国科学（A辑）
2005年 第2期

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