The Orchard crossing number of an abstract graph

TL;DR

This paper introduces the Orchard crossing number, a new graph invariant similar to the rectilinear crossing number, computes it for simple graphs, and explores its properties and variants.

Contribution

It defines the Orchard crossing number, analyzes its properties, and establishes connections with the rectilinear crossing number for specific graph families.

Findings

Computed Orchard crossing number for simple graphs

Proved properties of the Orchard crossing number

Defined and analyzed a related variant

Abstract

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.