The Orchard crossing number of an abstract graph

Details The Orchard crossing number of an abstract graph The Orchard crossing number of an abstract graph

2003-03-25

arxiv.org/abs/math/0303317v2

Mathematics

Combinatorics

17 pages, 10 figures. Totally revised, new material added. Submitted

Scientific paper

We introduce the Orchard crossing number, which is defined in a similar way to the well-known rectilinear crossing number. We compute the Orchard crossing number for some simple families of graphs. We also prove some properties of this crossing number. Moreover, we define a variant of this crossing number which is tightly connected to the rectilinear crossing number, and compute it for some simple families of graphs.

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