On the rectilinear crossing number of complete balanced multipartite graphs and layered graphs
arxiv(2024)
摘要
A rectilinear drawing of a graph is a drawing of the graph in the plane in
which the edges are drawn as straight-line segments. The rectilinear crossing
number of a graph is the minimum number of pairs of edges that cross over all
rectilinear drawings of the graph. Let n ≥ r be positive integers. The
graph K_n^r, is the complete r-partite graph on n vertices, in which
every set of the partition has at least ⌊ n/r ⌋ vertices. The
layered graph, L_n^r, is an r-partite graph on n vertices, in which for
every 1≤ i ≤ r-1, all the vertices in the i-th partition are adjacent
to all the vertices in the (i+1)-th partition. In this paper, we give upper
bounds on the rectilinear crossing numbers of K_n^r and L_n^r.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要