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Digital Object Identifier (DOI) 10.1007/s002090000152 Math. Z. 235, 315334 (2000)

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
Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden
(e-mail: athana@math.kth.se)
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA
(e-mail: edelman@math.umn.edu; reiner@math.umn.edu)
Received April 6, 1999 / in final form October 1, 1999 /
Published online July 20, 2000 c Springer-Verlag 2000
Abstract. We investigate the vertex-connectivity of the graph of f-mono-
tone paths on a d-polytope 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 2-connected for any d-polytope 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 re-examine the Baues problem for cellular strings on polytopes,


Source: Athanasiadis, Christos - Department of Mathematics, University of Athens


Collections: Mathematics