 
Summary: Digital Object Identifier (DOI) 10.1007/s002090000152
Math. Z. 235, 315334 (2000)
Monotone paths on polytopes
Christos A. Athanasiadis1, Paul H. Edelman2, Victor Reiner2
1
Department of Mathematics, Royal Institute of Technology, S100 44 Stockholm, Sweden
(email: athana@math.kth.se)
2
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA
(email: edelman@math.umn.edu; reiner@math.umn.edu)
Received April 6, 1999 / in final form October 1, 1999 /
Published online July 20, 2000 c SpringerVerlag 2000
Abstract. We investigate the vertexconnectivity of the graph of fmono
tone paths on a dpolytope P with respect to a generic functional f. The
third author has conjectured that this graph is always (d  1)connected.
We resolve this conjecture positively for simple polytopes and show that the
graph is 2connected for any dpolytope with d 3. However, we disprove
the conjecture in general by exhibiting counterexamples for each d 4 in
which the graph has a vertex of degree two.
We also reexamine the Baues problem for cellular strings on polytopes,
