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

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Thursday, July 26, 2018, 12:15 pm

**Duration**: 30 minutes

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

**Speaker**: Uli Wagner (IST Austria)

Consider a pure 2-dimensional simplicial complex X (in other words, a 3-uniform hypergraph). A shelling of X is an inductive procedure of building X by adding the triangles of X one at a time, in such a way that each new triangle (except the first one) intersects the previously constructed complex in a connected 1-dimensional piece (consisting of one, two, or all three edges on the boundary of the triangle); X is called shellable if has a shelling. The definition naturally generalizes to higher-dimensional complexes.

Shellings and shellability are fundamental concepts in a variety of areas including polytope theory (the boundary of every convex polytope is shellable, by a theorem of Brugesser and Mani), piecewise-linear topology, topological combinatorics, and others. One reason for its importance is that shellability – a purely combinatorial property – has strong topological consequences. For instance if a d-dimensional complex X is shellable and moreover a pseudomanifold (i.e., if every (d-1)-simplex of X contained in exactly two d-simplices, which is easily checked) then X is homeomorphic to a d-dimensional sphere – a property that is algorithmically undecidable for d\geq 5.

From a computational viewpoint, it is a natural question (raised at least as early as in the 1970’s by Danaraj ad Klee) whether one can decide efficiently whether a given complex is shellable. We settle this in the negative (modulo P\neq NP) and show that shellability of d-dimensional complexes is NP-complete for every d\geq 2.

Joint work with Xavier Goaoc, Pavel Paták, Zuzana Patáková, and Martin Tancer

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