有向图中的内在连接

IF 0.5 4区数学 Q3 MATHEMATICS

Osaka Journal of Mathematics Pub Date : 2015-07-01 DOI:10.18910/57670

Joel Foisy, H. Howards, N. Rich

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引用次数: 4

摘要

我们将内在连接的概念扩展到有向图。给出了构造内在联系有向图的方法，以及非内在联系的复杂有向图的方法。我们证明了图G的双有向形式是内在相连的当且仅当G是内在相连的。一个推论是J6, 6个顶点(有30条有向边)的完全对称有向图，是内在联系的。我们进一步推广这一点，证明通过删除6条边可以找到J6的子图，但删除7条边得到的J6子图没有内在连接。我们还证明了删除任意一条边的J6具有内在链接，但如果选择错误的两条边，则删除两条边的J6可以无链接嵌入。

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INTRINSIC LINKING IN DIRECTED GRAPHS

We extend the notion of intrinsic linking to directed graphs. We give methods of constructing intrinsically linked directed graphs, as well as complicated directed graphs that are not intrinsically linked. We prove that the double directed version of a graph G is intrinsically linked if and only if G is intrinsically linked. One Corollary is that J6, the complete symmetric directed graph on 6 vertices (with 30 directed edges), is intrinsically linked. We further extend this to show that it is possible to find a subgraph of J6 by deleting 6 edges that is still intrinsically linked, but that no subgraph of J6 obtained by deleting 7 edges is intrinsically linked. We also show that J6 with an arbitrary edge deleted is intrinsically linked, but if the wrong two edges are chosen, J6 with two edges deleted can be embedded linklessly.

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来源期刊

Osaka Journal of Mathematics 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Osaka Journal of Mathematics is published quarterly by the joint editorship of the Department of Mathematics, Graduate School of Science, Osaka University, and the Department of Mathematics, Faculty of Science, Osaka City University and the Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University with the cooperation of the Department of Mathematical Sciences, Faculty of Engineering Science, Osaka University. The Journal is devoted entirely to the publication of original works in pure and applied mathematics.