Crossing number (graph theory)

Known as: Crossing numberÂ
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, aâ€¦Â (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 withâ€¦Â (More)
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2009
2009
• Algorithmica
• 2009
A nonplanar graph G is near-planar if it contains an edge e such that Gâˆ’e is planar. The problem of determining the crossingâ€¦Â (More)
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Highly Cited
2007
Highly Cited
2007
• STOC
• 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 atâ€¦Â (More)
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2007
2007
• ISAAC
• 2007
CrossingNumber is one of the most challenging algorithmic problems in topological graph theory, with applications to graphâ€¦Â (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 reductionâ€¦Â (More)
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2005
2005
• Computing
• 2005
Let (G) denote the rectilinear crossing number of a graph G. We determine (K11)=102 and (K12)=153. Despite the remarkable huntâ€¦Â (More)
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2004
2004
• J. Comb. Theory, Ser. B
• 2004
The crossing number crÃ°GÃž of a graph G is the minimum possible number of edge crossings in a drawing of G in the plane, while theâ€¦Â (More)
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Highly Cited
1998
Highly Cited
1998
• J. Comb. Theory, Ser. B
• 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 arcâ€¦Â (More)
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1994
1994
• Symposium on Computational Geometry
• 1994
We show that any graph of <italic>n</italic> vertices that can be drawn in the plane with no <italic>k</italic>+1 pairwiseâ€¦Â (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)jâ€¦Â (More)
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