| Hamilton非二部图的弱泛圈性 |
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| 引用本文： | 何方国,胡智全. Hamilton非二部图的弱泛圈性[J]. 系统科学与数学, 2008, 28(10): 1288-1296 |
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| 作者姓名： | 何方国 胡智全 |
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| 作者单位： | 1. 华中科技大学系统工程研究所,武汉,430074
2. 华中师范大学数学与统计学学院,武汉,430074 |
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| 摘 要： | 图G称为弱泛圈图是指G包含了每个长为t(g(V)≤l≤c(G))的圈,其中g(G),c(v)分别是G的围长与周长.1997年Brandt提出以下猜想:边数大于[n2/4]-n 5的n阶非二部图为弱泛圈图.1999年Bollobas和Thomason证明了边数不小于[n2/4]-n 59的n阶非二部图为弱泛圈图.作者证明了如下结论:设G是n阶Hamilton非二部图,若G的边数不小于[n2/4]-n 12,则G为弱泛圈图.
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| 关 键 词： | 非二部图 Hamilton图 圈 弱泛圈图 |
| 收稿时间： | 2006-03-28 |
| 修稿时间： | 2007-09-17 |
A Weakly Pancyclic Theorem for Hamiltonian Non-Bipartite Graphs |
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| HE Fangguo,HU Zhiquan. A Weakly Pancyclic Theorem for Hamiltonian Non-Bipartite Graphs[J]. Journal of Systems Science and Mathematical Sciences, 2008, 28(10): 1288-1296 |
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| Authors: | HE Fangguo HU Zhiquan |
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| Affiliation: | (1)Institute of Systems Engineering, Huazhong University of Science & Technology, Wuhan 430074; (2)School of Mathematics and Statistics, Central China Normal University, Wuhan 430074. |
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| Abstract: | An n-vertex graph is called weakly pancyclic if it contains cycles of all lengths between its girth and circumference. In 1977, Brandt conjectured that an n-vertex non-bipartite graph with more than lfloor {{textstyle{{n^2 } over 4}}}rfloor- n + 5 edges is weakly pancyclic. Bollobas and Thomason(1999) proved that every non-bipartite graph of order n and size at least lfloor{{{textstyle{{n^2 } over 4}}}rfloor - n + 59 is weakly pancyclic. In this paper, the following result is established: let G be a Hamiltonian non-bipartite graph of order $n$ and size at least lfloor {{textstyle{{n^2 } over 4}}}rfloor - n + 12, then G is weakly pancyclic. |
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| Keywords: | Non-bipartite graph Hamiltonian graph cycle weakly pancyclic graph. |
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