Crossing number (graph theory)

Known as: Crossing number 
In graph theory, the crossing number cr(G) of a graph G is the lowest number of edge crossings of a plane drawing of the graph G. For instance, a… (More)
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2011
2011
We study the Minimum Crossing Number problem: given an n-vertex graph G, the goal is to find a drawing of G in the plane with… (More)
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2009
2009
A nonplanar graph G is near-planar if it contains an edge e such that G−e is planar. The problem of determining the crossing… (More)
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Highly Cited
2007
Highly Cited
2007
We show that for every fixed k, there is a linear time algorithm that decides whether or not a given graph has crossing number at… (More)
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2007
2007
CrossingNumber is one of the most challenging algorithmic problems in topological graph theory, with applications to graph… (More)
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Highly Cited
2006
Highly Cited
2006
It was proved by [Garey and Johnson, 1983] that computing the crossing number of a graph is an NP -hard problem. Their reduction… (More)
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2005
2005
Let (G) denote the rectilinear crossing number of a graph G. We determine (K11)=102 and (K12)=153. Despite the remarkable hunt… (More)
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2004
2004
The crossing number crðGÞ of a graph G is the minimum possible number of edge crossings in a drawing of G in the plane, while the… (More)
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Highly Cited
1998
Highly Cited
1998
A drawing of a graph G is a mapping which assigns to each vertex a point of the plane and to each edge a simple continuous arc… (More)
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1994
1994
We show that any graph of <italic>n</italic> vertices that can be drawn in the plane with no <italic>k</italic>+1 pairwise… (More)
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1993
1993
Zarankiewicz's conjecture, that the crossing number of the completebipartite graph K,,,, is [$ rnllfr (m 1)Jl; n j [$ ( n 1)j… (More)
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