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几乎完全分部图是本质链环图的一个充分条件
A Sufficient Condition for Intrinsic Linking of Almost Complete Partite Graphs

李阳
LI Yang

北京工商大学应用数学系, 北京, 100048
Department of Applied Mathematics,Beijing Technology and Business University, Beijing, 100048, P. R. China

收稿日期: 2013-10-29
出版日期: 2014-07-25
DOI: 10.11845/sxjz.2013143b

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摘要 设$G$是去掉两条边的完全$p$-部图$(pleq3)$,且是本质纽结图,经过有限次$Delta$-$Y$变换或点扩张得到图$J$.本文证明了,若从$J$中去掉任一顶点及与其相关联的所有边,则所得的图为一个本质链环图.这一结果给出了更多的本质纽结图满足Adams的纽结书中所提出的经典猜想``去掉本质纽结图的任一顶点得到的一定是本质链环图''.
关键词 本质纽结图本质链环图$Delta$-$Y$变换嵌入图    
Abstract:We provide evidence in support of a conjecture presented in Adams' ``The Knot Book'' that the removal of any vertex and all edges incident to that vertex from an intrinsically knotted graph yields an intrinsically linked graph.In this paper, we prove that Adams' conjecture holds for J when G is a complete $p$-partite graph with 2 edges removed, $pleq 3$,and intrinsically knotted, and $J$ represents any graph obtained from $G$ by a finite sequence of $Delta$-$Y$ exchanges and/or vertex expansions.
Key words intrinsically linked graph    $Delta $-$Y$ exchange    embedded graph
基金资助:The work is supported by Scientific Research Common Program of Beijing Municipal Commission of Education (No.KM201410011006), the Research Foundation for Youth Scholars of BTBU (No.QNJJ2012-26) and BNSF (No.1132002, No.1122013).
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