| 与直径和围长有关的最大亏格的下界 |
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| 引用本文： | 盛秀艳. 与直径和围长有关的最大亏格的下界[J]. 数学学报, 2004, 47(6): 1201-120. DOI: cnki:ISSN:0583-1431.0.2004-06-019 |
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| 作者姓名： | 盛秀艳 |
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| 作者单位： | 聊城大学数学科学学院,聊城,252059 |
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| 基金项目： | 重庆市教委科研基金项目(010204) |
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| 摘 要： | 本文证明了如下结果:设G为直径为d的简单图,若G的围长不小于d,则当d为不小于4的偶数时,有ξ(G)≤1,即G是上可嵌入的;当d为不小于3的奇数时,有ξ(G)≤2,即γM(G)≥1/2β(G)-1.
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| 关 键 词： | Betti亏数 上可嵌入性 最大亏格 |
| 文章编号： | 0583-1431(2004)06-1201-04 |
The Lower Bounds of the Maximum Genus on Graphs in Terms of Diameter and Girth |
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| Xiu Yan SHENG. The Lower Bounds of the Maximum Genus on Graphs in Terms of Diameter and Girth[J]. Acta Mathematica Sinica, 2004, 47(6): 1201-120. DOI: cnki:ISSN:0583-1431.0.2004-06-019 |
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| Authors: | Xiu Yan SHENG |
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| Affiliation: | Xiu Yan SHENG (Department of Mathematical Science, Liaocheng University, Liaocheng 252059, P. R. China) |
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| Abstract: | This paper proves the following results: Let G be a simple graph with diameter d. If its girth is not less than d, then the Betti deficient number of G, ξ(G)≤1, when d (≥4) is even, i.e. G is upper embeddable; and the Betti deficient number of G, ξ(G)≤2, when d (≥3) is odd, i.e. the maximum genus of G, γM(G)≥1/2β(G) - 1. |
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| Keywords: | Betti deficiency number Upper embeddable Maximum genus |
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