论文标题
三角形中的配对和半段统治
Paired and semipaired domination in triangulations
论文作者
论文摘要
一组托管$ g $是一个子集$ d $的顶点，因此每个顶点在$ d $中至少在$ d $中至少一个顶点。如果其顶点引起的子图具有完美的匹配，则将配对一个主导的集合$ d $，如果$ d $中的每个顶点都与距离距离2范围内的$ d $中的另一个顶点配对，则半仪。由$γ_{pr}（g）$表示的配对支配数是$ g $的配对主导套件的最低基数，并且半单位统治编号，用$γ_{pr2}（g）$表示，是$ g $ $ g $的半主导型组的最小基数。几乎三角形的是双连接的平面图，该图的平面图承认了一个嵌入的平面，使其所有的脸都是三角形的，除了外脸外。我们在本文中表明$γ_{pr}（g）\ le 2 \ lfloor \ frac {n} {n} {4} {4} \ rfloor $对于任何接近triangulation $ n \ ge 4 $ of triangulation $ g $ g ge 4 $ $ \ rfloor $ for任何近三角测量$ g $的订单$ n \ ge 5 $。
A dominating set of a graph $G$ is a subset $D$ of vertices such that every vertex not in $D$ is adjacent to at least one vertex in $D$. A dominating set $D$ is paired if the subgraph induced by its vertices has a perfect matching, and semipaired if every vertex in $D$ is paired with exactly one other vertex in $D$ that is within distance 2 from it. The paired domination number, denoted by $γ_{pr}(G)$, is the minimum cardinality of a paired dominating set of $G$, and the semipaired domination number, denoted by $γ_{pr2}(G)$, is the minimum cardinality of a semipaired dominating set of $G$. A near-triangulation is a biconnected planar graph that admits a plane embedding such that all of its faces are triangles except possibly the outer face. We show in this paper that $γ_{pr}(G) \le 2 \lfloor \frac{n}{4} \rfloor$ for any near-triangulation $G$ of order $n\ge 4$, and that with some exceptions, $γ_{pr2}(G) \le \lfloor \frac{2n}{5} \rfloor$ for any near-triangulation $G$ of order $n\ge 5$.
