The toroidal crossing number of the complete graph
نویسندگان
چکیده
منابع مشابه
META-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 ...
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Abstract: The well known Zarankiewicz’ conjecture is said that the crossing number of the complete bipartite graph Km,n (m ≤ n) is Z(m, n), where Z(m,n) = ⌊ m 2 ⌋⌊ 2 ⌋⌊ 2 ⌋ ⌊ 2 ⌋ (for any real number x, ⌊x⌋ denotes the maximal integer no more than x). Presently, Zarankiewicz’ conjecture is proved true only for the case m ≤ 6. In this article, the authors prove that if Zarankiewicz’ conjecture h...
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CrossingNumber is one of the most challenging algorithmic problems in topological graph theory, with applications to graph drawing and VLSI layout. No polynomial time approximation algorithm is known for this NP-Complete problem. We give in this paper a polynomial time approximation algorithm for the crossing number of toroidal graphs with bounded degree. In course of proving the algorithm we p...
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It is shown that if a graph of n vertices can be drawn on the torus without edge crossings and the maximum degree of its vertices is at most d, then its planar crossing number cannot exceed cdn, where c is a constant. This bound, conjectured by Brass, cannot be improved, apart from the value of the constant. We strengthen and generalize this result to the case when the graph has a crossing-free...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory
سال: 1968
ISSN: 0021-9800
DOI: 10.1016/s0021-9800(68)80063-8