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Pure Mathematics 2024
包装两个边数总和为2n-2的n阶图对(II)——{(p,p-2),(p,p)}图对包装
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Abstract:
图的包装问题是图论近几十年来较关注的问题之一。在理论上,它为研究图论中一些经典问题提供新的方式。在应用上,对计算机、生物信息、电路设计等领域的发展有举足轻重的意义,其在对离散系统和网络系统的空间和容量利用等方面具有实际性帮助。本文给出边数总和为2n?2的n阶图对{(p,p?2),(p,p)}包装的充要条件。
The packing problem of graphs is one of the most concerned problems in graph theory in recent decades. Theoretically, it provides a new way to study some classical problems in graph theory. In terms of application, it is of great significance to the development of the computer, biological information and circuit design field, and is of practical help to the space and capacity utilization of discrete systems and network systems. In this paper, it has been proved that the necessary and sufficient conditions for packing pairs of(p,p?2)-graphs and(p,p)-graphs of the n order whose sum of edges is 2n?2.
[1] | Yap, H.P. (1986) Some Topics in Graph Theory. The Press Syndicate of the University of Cambridge, London. |
[2] | 方新贵, 王敏. 关于包装(p, p?1)图对的Slater问题[J]. 烟台大学学报(自然科学与工程版), 1988(1): 15-18. |
[3] | 唐干武, 赵翌, 王敏. Erd?s-Sós猜想的一个结果[J]. 西南师范大学学报(自然科学版), 2009, 34(1): 24-27. |
[4] | 罗奇. 包装两个边数总和为2n?2的n阶图对(I)——{(p, p?1), (p, p?1)}图对包装[J]. 桂林师范高等专科学校学报, 2021, 140(6): 92-95. |
[5] | J.A.邦迪, U.S.R.默蒂. 图论及其应用[M]. 北京: 科学出版社, 1987. |
[6] | 方新贵, 王敏. 包装{(p, p?1), (p, p)}图对和Slater问题[J]. 系统科学与数学, 1989, 9(2): 133-137. |
[7] | 唐干武, 王敏. 包装(p, p?2)图和不含K3的(p, p 1)图[J]. 江西师范大学学报, 2005, 29(3): 220-223. |