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Maximum Rectilinear Crossing Number of Uniform Hypergraphs
We improve the lower bound on the d -dimensional rectilinear crossing number of the complete d -uniform hypergraph having 2 d vertices to
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Rectilinear Crossings in Complete Balanced d-Partite d-Uniform Hypergraphs
In this paper, we study the embedding of a complete balanced d -partite d -uniform hypergraph with its nd vertices represented as points in general...
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Strong Edge Coloring of Outerplane Graphs with Independent Crossings
The strong chromatic index of a graph is the minimum number of colors needed in a proper edge coloring so that no edge is adjacent to two edges of...
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Combinatorial Properties and Recognition of Unit Square Visibility Graphs
Unit square visibility graphs (USV) are described by axis-parallel visibility between unit squares placed in the plane. If the squares are required...
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Atomistic Simulation of the Coexistence of Liquid–Vapor Phase States for Gold and Determination of Critical Parameters
AbstractThe work is devoted to the study (on the example of gold) of the properties of metals near the critical point. Long-term studies testify to...
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Generalization of the Conway–Gordon Theorem and Intrinsic Linking on Complete Graphs
Conway and Gordon proved that for every spatial complete graph on six vertices, the sum of the linking numbers over all of the constituent...
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Boundary Crossing Problems for Compound Renewal Processes
We find sharp asymptotics of the probability that the trajectory of a compound renewal process crosses (or does not cross) an arbitrary remote...
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Aircraft Conflict Resolution
Air traffic management (ATM) represents a domain of challenging applications of mathematical optimization.
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Twisted Ways to Find Plane Structures in Simple Drawings of Complete Graphs
Simple drawings are drawings of graphs in which the edges are Jordan arcs and each pair of edges share at most one point (a proper crossing or a...
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Inserting One Edge into a Simple Drawing is Hard
A simple drawing D ( G ) of a graph G is one where each pair of edges share at most one point: either a common endpoint or a proper crossing. An edge e ...
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On crossing families of complete geometric graphs
A crossing family is a collection of pairwise crossing segments, this concept was introduced by Aronov et al. [
4 ]. They proved that any set of n ... -
(Re)packing Equal Disks into Rectangle
The problem of packing of equal disks (or circles) into a rectangle is a fundamental geometric problem. (By a packing here we mean an arrangement of...
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SCIP-Jack: An Exact High Performance Solver for Steiner Tree Problems in Graphs and Related Problems
The Steiner tree problem in graphs is one of the classic combinatorial optimization problems. Furthermore, many related problems, such as the...
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Subsymmetries of the Wallpaper Groups in Architecture and Urban Designs
Wallpaper patterns are commonly used in architecture and decorative art, regardless of region and culture. An interesting consequence is that the...
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