Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, November 06, 2014, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Michael Hoffmann

Arc Diagrams, Flip Distances, and Hamiltonian Triangulations

We show that every triangulation (maximal planar graph) on n >= 6 vertices can be flipped into a Hamiltonian triangulation using a sequence of less than n/2 combinatorial edge flips. The previously best upper bound uses 4-connectivity as a means to establish Hamiltonicity. But in general about 3n/5 flips are necessary to reach a 4-connected triangulation. Our result improves the upper bound on the diameter of the combinatorial flip graph of triangulations on n vertices from 5.2n − 33.6 to 5n − 23. We also show that for every triangulation on n vertices there is a simultaneous flip of less than 2n/3 edges to a 4-connected triangulation. The bound on the number of edges is tight, up to an additive constant. As another application we show that every planar graph on n vertices admits an arc diagram with less than n/2 biarcs, that is, after subdividing less than n/2 (of potentially 3n − 6) edges the resulting graph admits a 2-page book embedding.

Joint work with Jean Cardinal, Vincent Kusters, Csaba Tóth, and Manuel Wettstein.

Upcoming talks     |     All previous talks     |     Talks by speaker     |     Upcoming talks in iCal format (beta version!)

Previous talks by year:   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