# Geometry Seminar

#### Results on and around Generalized Twisted Drawings of Complete Graphs

**Speaker:**
Birgit Vogtenhuber, TU Graz

**Location:**
Online

**Videoconference link:** https://youtu.be/r5J0mfXlbRw

**Date:**
Tuesday, April 2, 2024, 2 p.m.

**Synopsis:**

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 common endpoint). A simple drawing is generalized twisted if there is a point O such that every ray emanating from O crosses every edge of the drawing at most once and there is a ray emanating from O which crosses every edge exactly once.

In this talk we will survey recent results on and around this special kind of simple drawings. We will present several structural properties and characterizations of generalized twisted drawings. Further, we will sketch how generalized twisted drawings can be used to find plane substructures in simple drawings of complete graphs. We will finish with a number of interesting open problems.

**Notes:**

See mailing list announcements for Zoom details or contact Boris Aronov.