Drawing complete multipartite graphs on the plane with restrictions on crossings
نویسنده
چکیده
We introduce the concept of NIC-planar graphs and present the full characterization of NIC-planar complete k-partite graphs.
منابع مشابه
On Crossing Numbers of Complete Tripartite and Balanced Complete Multipartite Graphs
The crossing number cr(G) of a graph G is the minimum number of crossings in a nondegenerate planar drawing of G. The rectilinear crossing number cr(G) of G is the minimum number of crossings in a rectilinear nondegenerate planar drawing (with edges as straight line segments) of G. Zarankiewicz proved in 1952 that cr(Kn1,n2) ≤ Z(n1, n2) := ⌊ n1 2 ⌋ ⌊ n1−1 2 ⌋ ⌊ n2 2 ⌋ ⌊ n2−1 2 ⌋ . We define an ...
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The crossing number cr(G) of a graph G is the minimum number of crossings in a nondegenerate planar drawing of G. The rectilinear crossing number cr(G) of G is the minimum number of crossings in a rectilinear nondegenerate planar drawing (with edges as straight line segments) of G. Zarankiewicz proved in 1952 that cr(Kn1,n2) ≤ Z(n1, n2) := ⌊ n1 2 ⌋ ⌊ n1−1 2 ⌋ ⌊ n2 2 ⌋ ⌊ n2−1 2 ⌋ . We define an ...
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Let G be a graph on n vertices; let S be a set of n points in general position (no three of them collinear) in the plane. A rectilinear drawing of G is a drawing of G in the plane that satisfies the following. Its vertices are points in general position and its edges are drawn as straight line segments. The number of crossings of a rectilinear drawing is the number of pairs of its edges that cr...
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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 ...
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عنوان ژورنال:
- CoRR
دوره abs/1311.1994 شماره
صفحات -
تاریخ انتشار 2013