| 恰含5条非基本边的极小3连通图 |
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| 引用本文： | 陈仪朝,苏健基.恰含5条非基本边的极小3连通图[J].广西师范大学学报(自然科学版),2004,22(3):29-34. |
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| 作者姓名： | 陈仪朝 苏健基 |
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| 作者单位： | 广西师范大学,数学与计算机科学学院,广西,桂林,541004;广西师范大学,数学与计算机科学学院,广西,桂林,541004 |
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| 基金项目： | 国家自然科学基金资助项目 ( 1 0 1 71 0 2 2 ) |
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| 摘 要： | 简单极小3连通图G中的一条不在任何三边形中的边e收缩之后所得到的图如果仍3连通，则称e为G的非基本边．Oxley与wu证明不是轮的简单极小3连通图至少包含3条非基本边，并且刻画了恰含3条或4条非基本边的不是轮的简单极小3连通图．现刻画恰含5条非基本边的不是轮的简单极小3连通图，它们是13类特殊的图．
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| 关 键 词： | 图论 极小3连通图 可收缩边 非基本边 扇 |
| 文章编号： | 1001-6600(2004)03-0029-06 |
MINIMALLY 3-CONNECTED GRAPHS WITH EXACTLY FIVE NON-ESSENTIAL EDGES |
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| CHEN Yi-chao,SU Jian-ji.MINIMALLY 3-CONNECTED GRAPHS WITH EXACTLY FIVE NON-ESSENTIAL EDGES[J].Journal of Guangxi Normal University(Natural Science Edition),2004,22(3):29-34. |
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| Authors: | CHEN Yi-chao SU Jian-ji |
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| Abstract: | Let G be a simple 3-connected graph.An edge e of G is called deletable if the deletion G-e is 3-connected.A contractible edge e of G is an edge whose contraction yields again a 3-connected graph.If an edge e of G is not in any triangle and is contractible,then call e simple contractible edge of G.Tutte called an edge essential if it is neither deletable nor simple-contractible.Oxley and Wu proved:that if G is a minimally 3-connected graph other than a wheel then G has at least three non-essential edges,and moreover,G has exactly three non-essential edges if and only if G is a split-wheel or a crossed split-wheel,G has exactly four non-essential edges if and only if a three fan or a doubly interlocked wheel.This paper specifies all such minimally 3-connected graphs with exactly 5 non-essential edges. |
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| Keywords: | graph theory minimally 3-connected contractible edge non-essential edge fan |
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