论文标题
边缘一般位置问题的概括
Generalization of edge general position problem
论文作者
论文摘要
图$ g $的边缘地球封面问题是找到覆盖$ g $的边缘集的最小数量的大地测量学。 Edge $ k $ - 一般位置问题被引入了一个问题，以找到最大的$ g $ $ g $的$ s $ s $，以至于$ s $ s $的$ k-1 $边缘在普通的大地测量上。我们研究了这种双重最大最大问题，并将它们连接到边缘地球分区问题。使用这些连接，针对$ k $的不同值以及包括圆环网络，超级立管和贝内斯网络在内的不同值确定边缘$ k $ - 一般位置编号的精确值。
The edge geodesic cover problem of a graph $G$ is to find a smallest number of geodesics that cover the edge set of $G$. The edge $k$-general position problem is introduced as the problem to find a largest set $S$ of edges of $G$ such that no $k-1$ edges of $S$ lie on a common geodesic. We study this dual min-max problems and connect them to an edge geodesic partition problem. Using these connections, exact values of the edge $k$-general position number is determined for different values of $k$ and for different networks including torus networks, hypercubes, and Benes networks.
