Elie Feder And
نویسنده
چکیده
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.
منابع مشابه
On the Orchard Crossing Number of the Complete Bipartite Graphs Kn,n
We compute the Orchard crossing number, which is defined in a similar way to the rectilinear crossing number, for the complete bipartite graphs Kn,n.
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This paper deals with the Orchard crossing number of some families of graphs which are based on cycles. These include disjoint cycles, cycles which share a vertex and cycles which share an edge. Specifically, we focus on the prism and ladder graphs.
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In this paper, we cope with the following problem: compute the size of the convex hull of a configuration C, where the given data is the number of separating lines between any two points of the configuration (where the lines are generated by pairs of other points of the configuration). We give an algorithm for the case that the convex hull is of size 3, and a partial algorithm and some directio...
متن کاملThe Maximum of the Maximum Rectilinear Crossing Numbers of d-Regular Graphs of Order n
We extend known results regarding the maximum rectilinear crossing number of the cycle graph (Cn) and the complete graph (Kn) to the class of general d-regular graphs Rn,d. We present the generalized star drawings of the d-regular graphs Sn,d of order n where n + d ≡ 1 (mod 2) and prove that they maximize the maximum rectilinear crossing numbers. A star-like drawing of Sn,d for n ≡ d ≡ 0 (mod 2...
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Let G be an abstract graph. Motivated by the Orchard relation, introduced in [3, 4], we have defined the Orchard crossing number of G [5], in a similar way to the well-known rectilinear crossing number of an abstract graph G (denoted by cr(G), see [1, 8]). A general reference for crossing numbers can be [6]. The Orchard crossing number is interesting for several reasons. First, it is based on t...
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