| λ'-最优无三角图的最小边度充分条件 |
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| 引用本文： | 刘爱霞,原军,吴红梅.λ'-最优无三角图的最小边度充分条件[J].太原科技大学学报,2014(4):318-321. |
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| 作者姓名： | 刘爱霞 原军 吴红梅 |
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| 作者单位： | 太原科技大学应用科学学院,太原030024 |
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| 基金项目： | 数学天元基金（11126067）; 山西省自然科学基金（2012021001-2）; 太原科技大学博士启动金（20082014） |
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| 摘 要： | 设S是连通图G的一个边割。若G-S不包含孤立点,则称S是G的一个限制边割。图G的最小限制边割的边数称为G的限制边连通度,记为λ'(G).如果图G的限制边连通度等于其最小度,则称图G是最优限制边连通的,简称λ'-最优的。设G是一个n阶的连通无三角图,且最小度δ(G)≥2.文章证明了,若最小边度ξ(G)≥(n/2-2 )(1+1/δ(G)-1),则G是λ'-最优的。并由此推出,若连通无三角图G的最小度δ(G)≥n/4+1,则G是λ'-最优的。最后给出例子说明这些结果给出的边界都是紧的。
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| 关 键 词： | 无三角图 边连通度 限制边连通度 |
The Minimum Edge Degree Conditions for Triangle-free Graphs Connectivity to be-optimal |
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| LIU Ai-xia,YUAN Jun,WU Hong-mei.The Minimum Edge Degree Conditions for Triangle-free Graphs Connectivity to be-optimal[J].Journal of Taiyuan University of Science and Technology,2014(4):318-321. |
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| Authors: | LIU Ai-xia YUAN Jun WU Hong-mei |
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| Institution: | (School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, China) |
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| Abstract: | An edge cut S of a connected graph G is called as a restricted edge cut,if G-S contains unisolated vertices.The minimum cardinality of all restricted edge cuts is called as the restricted edge connectivity of λ＇（G）.A graph G is optimally restricted edge-connected,for short λ＇-optimal,if λ＇（G） = ξ（G）,where ξ（G） is the minimum edge degree of G.A graph is thought to be super-restricted edge-connected,for short super-λ＇ if every minimum restricted edge cut isolates an edge.Let G be a connected triangle-free graph of order n and minimum degree δ（G≥2）,if the minimum edge degree ξ（G） ≥（n/2-2） （1 ＋1/δ（G）-1）,then G is λ＇-optimal.Using this result,we deduce that if the minimum degree of triangle-free graph G,δ（G） ≥n/4＋ 1,then G is λ＇-optimal.Finally,an example is presented to show that the bounds of these results are both tight. |
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| Keywords: | Triangle-free graphs edge connectivity restricted edge connectivity |
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