Crossing number (graph theory) - Wikipedia
In graph theory, the crossing number cr(G) of a graph G is the lowest number of edge crossings of a plane drawing of the graph G. For instance, a graph is planar if and only if its crossing number is zero.
Graph Crossing Number -- from Wolfram MathWorld
Given a "good" graph G (i.e., one for which all intersecting graph edges intersect in a single point and arise from four distinct graph vertices), the crossing number is the minimum possible number of crossings with which the graph can be drawn, including using curved (non-rectilinear) edges.
What is the crossing number? The crossing number of a graph G is the smallest number of pairwise crossings of edges among all drawings of G in the plane. In the last decade, there has been significant progress on a true theory of crossing numbers.
Starting with its introduction by Turán, we will discuss known results for complete and complete bipartite graphs. Then we will focus on some historical con-fusion on the crossing number that has been brought up by Pach and Tóth as well as Székely.
Abstract ― For any simple graph G = (V; E), we can de ̄ne four types of crossing number: crossing number, rectilinear crossing num-ber, odd-crossing number, and pairwise crossing number. We discuss the relationship of them. The concept “drawing”is de ̄ned in a variety of distinct ways in the literature.
The Crossing Number of Graphs: Theory and Computation
This survey concentrates on selected theoretical and computational aspects of the crossing number of graphs. Starting with its introduction by Turán, we will discuss known results for complete and complete bipartite graphs.
Essentially the crossing number of a graph is the minimum crossing number of any of its drawings. Furthermore we can define the rectilinear crossing number of a graph, ¯ν(G), the
Crossing Number (Graph) - Michigan State University
Given a ``good'' Graph (i.e., one for which all intersecting Edges intersect in a single point and arise from four distinct Vertices), the crossing number is the minimum possible number of crossings with which the Graph can be drawn. A Graph with crossing number 0 is a Planar Graph.
The crossing number of a graph is often denoted as k or cr. Among the six incarnations of the Petersen graph, the middle one in the bottom row exhibits just 2 fewer than any other in the collection. In fact, 2 is crossing number of Petersen graph. Try as you may, it is impossible to diagram the Petersen graph with one or zero crossings. The ...
[PDF] The Crossing Number - Semantic Scholar
We define the crossing number, a natural invariant in topological graph theory, and survey general results on the crossing number in the Euclidean plane. We also discuss progress on conjectures for two particular cases: complete bipartite graphs and complete graphs.
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