论文标题
投影平面图中的链接
Links in projective planar graphs
论文作者
论文摘要
如果$ g $具有无链接链接的投射平面嵌入，则图$ g $是不可分割的投影平面。未分离的投影平面图在未成年人的下关闭，是投射外平面图的超类。我们通过证明较小的最小非注射式平面图$ g $ $ g $是较小的最小分离的射影平面或$ g \ dot \ dot \ dot \ dot \ cup k_ {1} $是$ niminimal弱分离的平面$ G $ g $ G $ g $ g $是$ G $ G $ g $ g $ g $ g $ g $ g $ g $ g $ g $是$ g $ G $ G $ g $ G $是$ G $ G $ G $ G $是$ G $ G $ G $ G $ G $是$ G $ G $ G $ G $是$ G $ G $ G $，对于$ G $ G $ G $ G $是$ G $ G $， 概括分离投影平面图的一种方法是考虑由两个周期和一对顶点组成的I型3链接。图形是本质上投影的平面I型I型3链接（IPPI3L），如果其每个投影平面嵌入的每个嵌入式都包含一个非平地型I型3链接。我们通过将所有次要最小IPPI3L图与三个或更多组件分类，并找到许多其他组件较少的组件，从而部分表征了次要的IPPI3L图。
A graph $G$ is nonseparating projective planar if $G$ has a projective planar embedding without a nonsplit link. Nonseparating projective planar graphs are closed under taking minors and are a superclass of projective outerplanar graphs. We partially characterize the minor-minimal separating projective planar graphs by proving that given a minor-minimal nonouter-projective-planar graph $G$, either $G$ is minor-minimal separating projective planar or $G \dot\cup K_{1}$ is minor-minimal weakly separating projective planar, a necessary condition for $G$ to be separating projective planar. One way to generalize separating projective planar graphs is to consider type I 3-links consisting of two cycles and a pair of vertices. A graph is intrinsically projective planar type I 3-linked (IPPI3L) if its every projective planar embedding contains a nonsplit type I 3-link. We partially characterize minor-minimal IPPI3L graphs by classifying all minor-minimal IPPI3L graphs with three or more components, and finding many others with fewer components.
