منابع مشابه
Crossing Number Is Hard for Cubic Graphs
It was proved by [Garey and Johnson, 1983] that computing the crossing number of a graph is an NP -hard problem. Their reduction, however, used parallel edges and vertices of very high degrees. We prove here that it is NP -hard to determine the crossing number of a simple cubic graph. In particular, this implies that the minor-monotone version of crossing number is also NP -hard, which has been...
متن کاملCrossing Number is Hard for Kernelization
The graph crossing number problem, cr(G) ≤ k, asks for a drawing of a graph G in the plane with at most k edge crossings. Although this problem is in general notoriously difficult, it is fixedparameter tractable for the parameter k [Grohe]. This suggests a closely related question of whether this problem has a polynomial kernel, meaning whether every instance of cr(G) ≤ k can be in polynomial t...
متن کاملCrossing Number is Hard for Kernelization
The graph crossing number problem, cr(G) ≤ k, asks for a drawing of a graph G in the plane with at most k edge crossings. Although this problem is in general notoriously difficult, it is fixedparameter tractable for the parameter k [Grohe]. This suggests a closely related question of whether this problem has a polynomial kernel, meaning whether every instance of cr(G) ≤ k can be in polynomial t...
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 کاملOne Sided Crossing Minimization Is NP-Hard for Sparse Graphs
The one sided crossing minimization problem consists of placing the vertices of one part of a bipartite graph on prescribed positions on a straight line and finding the positions of the vertices of the second part on a parallel line and drawing the edges as straight lines such that the number of pairwise edge crossings is minimized. This problem represents the basic building block used for draw...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2006
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2005.09.009