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Rectilinear Local Crossing Number

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The rectilinear local crossing number of a graph G denoted lcr^_(G), is the minimum local crossing number over all rectilinear drawings of G.

Ábrego and Fernández-Merchant (2017) determined the rectilinear crossing number of the complete graph K_n to be

lcr^_(K_n)={4 for n=8; 15 for n=14; [1/2(n-3-[(n-3)/3])[(n-3)/2]] otherwise,
(1)

where [x] denotes the ceiling function.

See also

Graph Crossing Number, k-Planar Graph, Local Crossing Number, Rectilinear Crossing Number

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References

Ábrego, B. M. and Fernández-Merchant, S. "The Rectilinear Local Crossing Number of K_n." J. Combin. Th. Ser. A 151, 131-145, 2017.Lara, D.; Rubio-Montiel, C.; and Zaragoza, F. "Grundy and Pseudo-Grundy Indices for Complete Graphs." In Abstracts of the XVI Spanish Meeting on Computational Geometry. Barcelona, Spain: July 1-3, 2015.Sloane, N. J. A. Sequence A374243 in "The On-Line Encyclopedia of Integer Sequences."

Cite this as:

Weisstein, Eric W. "Rectilinear Local Crossing Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RectilinearLocalCrossingNumber.html

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