منابع مشابه
Crossing Angles of Geometric Graphs
We study the crossing angles of geometric graphs in the plane. We introduce the crossing angle number of a graph G, denoted can(G), which is the minimum number of angles between crossing edges in a straight-line drawing of G. We show that an n-vertex graph G with can(G) = O(1) has O(n) edges, but there are graphs G with bounded degree and arbitrarily large can(G). We also initiate the study of ...
متن کاملOn crossing numbers of geometric proximity graphs
Let P be a set of n points in the plane. A geometric proximity graph on P is a graph where two points are connected by a straight-line segment if they satisfy some prescribed proximity rule. We consider four classes of higher order proximity graphs, namely, the k-nearest neighbor graph, the k-relative neighborhood graph, the k-Gabriel graph and the k-Delaunay graph. For k = 0 (k = 1 in the case...
متن کاملOn disjoint crossing families in geometric graphs
A geometric graph is a graph drawn in the plane with vertices represented by points and edges as straight-line segments. A geometric graph contains a (k, l)-crossing family if there is a pair of edge subsets E1, E2 such that |E1| = k and |E2| = l, the edges in E1 are pairwise crossing, the edges in E2 are pairwise crossing, and every edges in E1 is disjoint to every edge in E2. We conjecture th...
متن کاملEncompassing colored crossing-free geometric graphs
Given n red and n blue points in the plane and a planar straight line matching between the red and the blue points, the matching can be extended into a bipartite planar straight line spanning tree. That is, any red-blue planar matching can be completed into a crossing-free red-blue spanning tree. Such a tree can be constructed in O(n log n) time. keywords: geometric graph, spanning tree, color
متن کاملGraphs That Admit Polyline Drawings with Few Crossing Angles
We consider graphs that admit polyline drawings where all crossings occur at the same angle α ∈ (0, π2 ]. We prove that every graph on n vertices that admits such a polyline drawing with at most two bends per edge has O(n) edges. This result remains true when each crossing occurs at an angle from a small set of angles. We also provide several extensions that might be of independent interest.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Graph Algorithms and Applications
سال: 2014
ISSN: 1526-1719
DOI: 10.7155/jgaa.00329