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UPPER BOUND THEOREM FOR ODD-DIMENSIONAL FLAG TRIANGULATIONS OF MANIFOLDS

Part of: Algebraic combinatorics Graph theory

Published online by Cambridge University Press:  01 June 2016

Michał Adamaszek  and
Jan Hladký
Michał Adamaszek
Affiliation:
Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark email aszek@mimuw.edu.pl
Jan Hladký
Affiliation:
Institute of Mathematics, Czech Academy of Science, Žıtná 25, 110 00, Praha, Czech Republic email honzahladky@gmail.com
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Abstract

We prove that among all flag triangulations of manifolds of odd dimension $2r-1$ , with a sufficient number of vertices, the unique maximizer of the entries of the $f$ -, $h$ -, $g$ - and $\unicode[STIX]{x1D6FE}$ -vector is the balanced join of $r$ cycles. Our proof uses methods from extremal graph theory.

MSC classification

Primary: 05E45: Combinatorial aspects of simplicial complexes 05C35: Extremal problems

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Type
Research Article
Information
Mathematika , Volume 62 , Issue 3 , 2016 , pp. 909 - 928
Copyright
Copyright © University College London 2016 

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