96-05: Subpolytopes of Cyclic Polytopes

DIMACS TR: 96-05

Subpolytopes of Cyclic Polytopes

Authors: Tibor Bisztriczky, Gyula Karolyi

ABSTRACT
A remarkable result of I. Shemer [4] states that the combinatorial structure of a neighbourly $2m$-polytope determines the combinatorial structure of each of its subpolytopes. From this, it follows that every subpolytope of a cyclic $2m$-polytope is cyclic. In this note, we present a direct proof of this consequence that also yields that certain subpolytopes of a cyclic $(2m+1)$-polytope are cyclic.

Paper Available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-05.ps.gz

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