There are no realizable 154- and 164configurations (2009)
ABSTRACT. There exist a finite number of natural numbers n for which we do not know whether a realizable n4-configuration does exist. We settle the two smallest unknown cases n = 15 and n = 16. In...
Edge-Graph Diameter Bounds for Convex Polytopes with Few Facets (2008)
We show that the edge graph of a 6-dimensional polytope with 12 facets has diameter at most 6, thus verifying the d-step conjecture of Klee and Walkup in the case of d=6. This implies that for all...
We show that no minimal vertex triangulation of a closed, connected, orientable 2-manifold of genus 6 admits a polyhedral embedding in R^3. We also provide examples of minimal vertex triangulations...
There are no realizable 15_4- and 16_4-configurations (2005)
Bokowski, Juergen, Schewe, Lars
There exist a finite number of natural numbers n for which we do not know whether a realizable n_4-configuration does exist. We settle the two smallest unknown cases n=15 and n=16. In these cases...