Crossing Numbers
نویسنده
چکیده
The crossing number of a graph G is the minimum number of crossings in a drawing of G. The determination of the crossing number is an NP-complete problem. We present two general lower bounds for the crossing number, and survey their applications and generalizations.
منابع مشابه
On the crossing numbers of Cartesian products with trees
Zip product was recently used in a note establishing the crossing number of the Cartesian product K1,n2Pm. In this paper, we further investigate the relations of this graph operation with the crossing numbers of graphs. First, we use a refining of the embedding method bound for crossing numbers to weaken the connectivity condition under which the crossing number is additive for the zip product....
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The crossing numbers of Cartesian products of paths, cycles or stars with all graphs of order at most four are known. For the path Pn of length n, the crossing numbers of Cartesian products G Pn for all connected graphs G on five vertices are also known. In this paper, the crossing numbers of Cartesian products G Pn for graphs G of order six are studied. Let H denote the unique tree of order si...
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The exact values of crossing numbers of the Cartesian products of four special graphs of order five with cycles are given and, in addition, all known crossing numbers of Cartesian products of cycles with connected graphs on five vertices are summarized.
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The simplest graph drawing method is that of putting the vertices of a graph on a line (spine) and drawing the edges as half-circles on k half planes (pages). Such drawings are called k-page book drawings and the minimal number of edge crossings in such a drawing is called the k-page crossing number. In a one-page book drawing, all edges are placed on one side of the spine, and in a two-page bo...
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There are known exact results of the crossing numbers of the Cartesian product of all graphs of order at most four with paths, cycles and stars. Moreover, for the path Pn of length n, the crossing numbers of Cartesian products G Pn for all connected graphs G on five vertices and for forty graphs G on six vertices are known. In this paper, we extend these results by determining the crossing numb...
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