Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Thursday, December 17, 2015, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Vincent Kusters

The planar tree packing theorem

Packing graphs is a combinatorial problem where several given graphs are being mapped into a common host graph such that every edge is used at most once. In the planar tree packing problem we are given two trees $T_1$ and $T_2$ on $n$ vertices and have to find a planar graph on $n$ vertices that is the edge-disjoint union of $T_1$ and $T_2$. A clear exception that must be made is the star which cannot be packed together with any other tree. But according to a conjecture of Garcia et al from 1997 this is the only exception, and all other pairs of trees admit a planar packing. Previous results addressed various special cases, such as a tree and a spider tree, a tree and a caterpillar, two trees of diameter four, two isomorphic trees, and trees of maximum degree three. Here we settle the conjecture in the affirmative and prove its general form, thus making it the planar tree packing theorem. The proof is constructive and provides a polynomial time algorithm to obtain a packing for two given non-star trees.

Joint work with Markus Geyer, Micheal Hoffmann, Micheal Kaufmann, and Csaba Toth.


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

Previous talks by year:   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