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

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Thursday, January 24, 2008, 12:15 pm

**Duration**: This information is not available in the database

**Location**: OAT S15/S16/S17

**Speaker**: Philipp Zumstein

A vertex k-coloring of a plane graph G is called polychromatic if in every face of G all k colors appear. Let p(G) be the maximum number k for which there is a polychromatic k-coloring.

For a plane graph G, let g(G) denote the length of the shortest face in G. We show p(G) >= (3g(G)-5)/4 and on the other hand for each g there is a graph with g(G) = g and p(G) <= (3g+1)/4.

Furthermore, the problem of determining whether a plane graph admits a vertex coloring by 3 colors in which all colors appear in every face is NP-complete even for graphs in which all faces are of length 3 or 4 only. If all faces are of length 3 this can be decided in polynomial time.

The investigation of this problem is motivated by its connection to a variant of the art gallery problem in computational geometry.

Joint work with Noga Alon, Robert Berke, Kevin Buchin, Maike Buchin, Peter Csorba, Saswata Shannigrahi, and Bettina Speckmann.

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