On the rectilinear crossing number of complete uniform hypergraphs
نویسندگان
چکیده
منابع مشابه
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 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 کاملMETA-HEURISTIC ALGORITHMS FOR MINIMIZING THE NUMBER OF CROSSING OF COMPLETE GRAPHS AND COMPLETE BIPARTITE GRAPHS
The minimum crossing number problem is among the oldest and most fundamental problems arising in the area of automatic graph drawing. In this paper, eight population-based meta-heuristic algorithms are utilized to tackle the minimum crossing number problem for two special types of graphs, namely complete graphs and complete bipartite graphs. A 2-page book drawing representation is employed for ...
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...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2017
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2016.11.001