Department of Computer Science | Institute of Theoretical Computer Science | CADMO
Prof. Emo Welzl and Prof. Bernd Gärtner
Mittagsseminar Talk Information |
Date and Time: Thursday, October 20, 2022, 12:15 pm
Duration: 30 minutes
Location: OAT S15/S16/S17
Speaker: Meghana M. Reddy
A graph is 2-planar if it has local crossing number two, that is, it can be drawn in the plane such that every edge has at most two crossings. A graph is maximal 2-planar if no edge can be added such that the resulting graph remains 2-planar. A 2-planar graph on n vertices has at most 5n-10 edges, and some (maximal) 2-planar graphs---referred to as optimal 2-planar---achieve this bound. However, in strong contrast to maximal planar graphs, a maximal 2-planar graph may have fewer than the maximum possible number of edges. In this paper, we determine the minimum edge density of maximal 2-planar graphs by proving that every maximal 2-planar graph on n vertices has at least 2n edges. We also show that this bound is tight, up to an additive constant. The lower bound is based on an analysis of the degree distribution in specific classes of drawings of the graph. The upper bound construction is verified by carefully exploring the space of admissible drawings using computer support. This is joint work with Michael Hoffmann.
Upcoming talks | All previous talks | Talks by speaker | Upcoming talks in iCal format (beta version!)
Previous talks by year: 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996
Information for students and suggested topics for student talks
Automatic MiSe System Software Version 1.4803M | admin login