AbstractWe give a new upper bound for the rectilinear crossing number cr¯(n) of the complete geometric graph Kn. We prove that cr¯(n)⩽0.380559(n4)+Θ(n3) by means of a new construction based on an iterative duplication strategy starting with a set having a certain structure of halving lines
The crossing number cr(G) of a graph G is the minimum number of crossings in a nondegenerate planar ...
The crossing number CR() of a graph =(,) is the smallest number of edge crossings over all drawi...
I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, includ...
AbstractWe give a new upper bound for the rectilinear crossing number cr¯(n) of the complete geometr...
AbstractScheinerman and Wilf (Amer. Math. Monthly 101 (1994) 939) assert that “an important open pro...
AbstractIt is shown that cr(Kn)⩽7n4 − 56n3 + 128n2 + 48nn − 73 + 108432 where cr(Kn) is the rectilin...
AbstractIt is shown that cr(Kn)⩽7n4 − 56n3 + 128n2 + 48nn − 73 + 108432 where cr(Kn) is the rectilin...
We give a new lower bound for the rectilinear crossing number cr(n) of the complete geometric graph ...
A straight-line drawing of a graph G is a mapping which assigns to each vertex a point in the plane ...
A straight-line drawing of a graph G is a mapping which assigns to each vertex a point in the plane ...
We prove a lower bound of 0.3288 n 4¡for the rectilinear crossing number cr(Kn) of a complete graph ...
We use circular sequences to give an improved lower bound on the minimum number of (<=k)-sets in a s...
A straight-line drawing of a graph G is a mapping which assigns to each vertex a point in the plane ...
AbstractThe toroidal crossing number of the complete graph on n points is shown to lie between23210(...
The crossing number cr(G) of a graph G is the minimum number of crossings in a nondegenerate planar ...
The crossing number cr(G) of a graph G is the minimum number of crossings in a nondegenerate planar ...
The crossing number CR() of a graph =(,) is the smallest number of edge crossings over all drawi...
I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, includ...
AbstractWe give a new upper bound for the rectilinear crossing number cr¯(n) of the complete geometr...
AbstractScheinerman and Wilf (Amer. Math. Monthly 101 (1994) 939) assert that “an important open pro...
AbstractIt is shown that cr(Kn)⩽7n4 − 56n3 + 128n2 + 48nn − 73 + 108432 where cr(Kn) is the rectilin...
AbstractIt is shown that cr(Kn)⩽7n4 − 56n3 + 128n2 + 48nn − 73 + 108432 where cr(Kn) is the rectilin...
We give a new lower bound for the rectilinear crossing number cr(n) of the complete geometric graph ...
A straight-line drawing of a graph G is a mapping which assigns to each vertex a point in the plane ...
A straight-line drawing of a graph G is a mapping which assigns to each vertex a point in the plane ...
We prove a lower bound of 0.3288 n 4¡for the rectilinear crossing number cr(Kn) of a complete graph ...
We use circular sequences to give an improved lower bound on the minimum number of (<=k)-sets in a s...
A straight-line drawing of a graph G is a mapping which assigns to each vertex a point in the plane ...
AbstractThe toroidal crossing number of the complete graph on n points is shown to lie between23210(...
The crossing number cr(G) of a graph G is the minimum number of crossings in a nondegenerate planar ...
The crossing number cr(G) of a graph G is the minimum number of crossings in a nondegenerate planar ...
The crossing number CR() of a graph =(,) is the smallest number of edge crossings over all drawi...
I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, includ...
DOI
Add to ORKG