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

Date and Time: Tuesday, April 28, 2009, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: David Avis (McGill Univ., Montreal)

The shelling property for polytopal digraphs

A polytopal digraph G(P) is an orientation of the skeleton of a convex polytope P. The possible non-degenerate pivot operations of the simplex method in solving a linear program over P can be represented as a special polytopal digraph known as an LP digraph. Presently there is no general characterization of which polytopal digraphs are LP digraphs, although three necessary properties are well known: acyclicity, unique sink orientation (USO), and the Holt-Klee property. We introduce a fourth property: the shelling property. For each d >= 4 and n >= d+2, we construct a polytopal digraph for a polytope P in dimension d with n vertices which is an acyclic USO that satisfies the Holt-Klee property, but does not satisfy the shelling property. Such examples cannot exist for other values of n and d.

Joint work with H. Miyata and S. Moriyama.

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