论文标题
本质上投影链接的图
Intrinsically projectively linked graphs
论文作者
论文摘要
如果图形在投影空间中的每个嵌入都包含一个非拼图链接，则图形本质上是项目链接（IPL）。以前已经找到了一些次要的IPL图。我们确定存在16个边缘上的次要iPl图，并通过将$δ-y $交换申请到$ k_ {7} -2e $来识别新的次要最小IPL图。我们证明，对于非对象 - 平面图$ g $，$ g+\ bar {k} _ {2} $是ipl，并描述了投影平面图$ g $上的必要和充分条件，使得$ g+g+\ bar {k} _ {2} $是ipl。最后，我们推断出$ f（g + \ bar {k_ {2}}）$的条件，以没有非链接，其中$ g $是投射平面，$ \ bar {k_ {2}} = \ {w_ {0} $\mathbb{R}P^{3}$ with $f(G)$ in $z=0$, $w_{0}$ above $z=0$, and $w_{1}$ below $z=0$ such that every edge connecting ${w_{0},w_{1}}$ to $G$ avoids the boundary of the 3-ball, whose antipodal points are identified to obtain投影空间。
A graph is intrinsically projectively linked (IPL) if its every embedding in projective space contains a nonsplit link. Some minor-minimal IPL graphs have been found previously. We determine that no minor-minimal IPL graphs on 16 edges exists and identify new minor-minimal IPL graphs by applying $Δ-Y$ exchanges to $K_{7}-2e$. We prove that for a nonouter-projective-planar graph $G$, $G+\bar{K}_{2}$ is IPL and describe the necessary and sufficient conditions on a projective planar graph $G$ such that $G+\bar{K}_{2}$ is IPL. Lastly, we deduce conditions for $f(G + \bar{K_{2}})$ to have no nonsplit link, where $G$ is projective planar, $\bar{K_{2}} = \{w_{0},w_{1}\}$, and $f(G + \bar{K_{2}})$ is the embedding onto $\mathbb{R}P^{3}$ with $f(G)$ in $z=0$, $w_{0}$ above $z=0$, and $w_{1}$ below $z=0$ such that every edge connecting ${w_{0},w_{1}}$ to $G$ avoids the boundary of the 3-ball, whose antipodal points are identified to obtain projective space.
