DeepAI AI Chat
Log In Sign Up

On the Maximum Number of Crossings in Star-Simple Drawings of K_n with No Empty Lens

by   Stefan Felsner, et al.

A star-simple drawing of a graph is a drawing in which adjacent edges do not cross. In contrast, there is no restriction on the number of crossings between two independent edges. When allowing empty lenses (a face in the arrangement induced by two edges that is bounded by a 2-cycle), two independent edges may cross arbitrarily many times in a star-simple drawing. We consider star-simple drawings of K_n with no empty lens. In this setting we prove an upper bound of 3((n-4)!) on the maximum number of crossings between any pair of edges. It follows that the total number of crossings is finite and upper bounded by n!.


page 1

page 2

page 3

page 4


β-Stars or On Extending a Drawing of a Connected Subgraph

We consider the problem of extending the drawing of a subgraph of a give...

On the number of edges of separated multigraphs

We prove that the number of edges of a multigraph G with n vertices is a...

Shooting Stars in Simple Drawings of K_m,n

Simple drawings are drawings of graphs in which two edges have at most o...

Star-Struck by Fixed Embeddings: Modern Crossing Number Heuristics

We present a thorough experimental evaluation of several crossing minimi...

The number of crossings in multigraphs with no empty lens

Let G be a multigraph with n vertices and e>4n edges, drawn in the plane...

Strong Hanani-Tutte for the Torus

If a graph can be drawn on the torus so that every two independent edges...

Improved Scheduling of Morphing Edge Drawing

Morphing edge drawing (MED), a graph drawing technique, is a dynamic ext...