Schrijver图SG(2k+2,k)的Hamilton性 |
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引用本文: | 李志江,陈玉军,刁科凤,王光辉.Schrijver图SG(2k+2,k)的Hamilton性[J].数学的实践与认识,2014(8). |
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作者姓名: | 李志江 陈玉军 刁科凤 王光辉 |
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作者单位: | 临沂大学沂水分校;临沂大学理学院;山东大学数学学院; |
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基金项目: | 国家自然科学基金(11101243);山东省自然科学基金(ZR2009AM013) |
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摘 要: | 通过图G的每个顶点的路称为Hamilton路,通过图G的每个顶点的圈称为Hamilton圈,具有Hamilton圈的图G称为Hamilton图.1952年Dirac曾得到关于Hamilton图一个充分条件的结论:图G有n个顶点,如果每个顶点υ满足:d(υ)≥n/2,则图G是Hamilton图.本文研究了Schrijver图SG(2k+2,k)的Hamilton性,采用寻找Hamilton圈的方法得出了Schrijver图SG(2k+2,k)是Hamilton图.
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关 键 词: | Schrijver图 均衡完全二部图 Hamilton图 圈 路 |
The Hamilton of Schrijver Graph SG(2k+2,k) |
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Abstract: | A path that contains every vertex of graph G is called a hamilton path,a hamilton cycle of G that contains every vertex of G,A graph is hamiltonian if it contains a hamilton cycle.Dirac had gotten a sufficient condition of the conclusion about hamiltonian in 1952:Graph G has n vertices,If each vertex v meet:d(v) ≥n/2,then G is a hamiltonian.In this paper,the hamilton of Schrijver graph SG(2k+2,k) is studied.It is obtained that the Schrijver graph SG(2k + 2,k) is a hamiltonian by the method of looking for Hamilton circle. |
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Keywords: | Schrijver graph balanced complete bipartite graph hamilton graph cycle path |
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