The Rectilinear Crossing Number of $K_{10}$ is $62$
نویسندگان
چکیده
منابع مشابه
The Rectilinear Crossing Number of K10 is 62
The rectilinear crossing number of a graph G is the minimum number of edge crossings that can occur in any drawing of G in which the edges are straight line segments and no three vertices are collinear. This number has been known for G = Kn if n ≤ 9. Using a combinatorial argument we show that for n = 10 the number is 62.
متن کاملMaximum Rectilinear Crossing Number
The problem of drawing a graph in the plane with a minimum number of edge crossings—called the crossing number of a graph—is a well-studied problem which dates back to the first half of the twentieth century, as mentioned in [11], and was formulated in full generality in [3]. It was shown that this problem is NP-Complete [4], and that it remains so even when restricted to cubic graphs [5]. Many...
متن کاملApproximating the Rectilinear Crossing Number
A straight-line drawing of a graph G is a mapping which assigns to each vertex a point in the plane and to each edge a straightline segment connecting the corresponding two points. The rectilinear crossing number of a graph G, cr(G), is the minimum number of pairs of crossing edges in any straight-line drawing of G. Determining or estimating cr(G) appears to be a difficult problem, and deciding...
متن کاملApproximating the Maximum Rectilinear Crossing Number
The problem of drawing a graph in the plane with a minimum number of edge crossings—called the crossing number of a graph—is a well-studied problem which dates back to the first half of the twentieth century, as mentioned in [11], and was formulated in full generality in [3]. It was shown that this problem is NP-Complete [4], and that it remains so even when restricted to cubic graphs [5]. Many...
متن کاملOn the structure of sets attaining the rectilinear crossing number ∗
We study the structural properties of the point configurations attaining the rectilinear crossing number cr(Kn), that is, those n-point sets that minimize the number of crossings over all possible straight-edge embeddings of Kn in the plane. As a main result we prove the conjecture that such sets always have a triangular convex hull. The techniques developed allow us to show a similar result fo...
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: The Electronic Journal of Combinatorics
سال: 2001
ISSN: 1077-8926
DOI: 10.37236/1567