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Discrete Mathematics & Theoretical Computer Science |
We prove that among all flag 3-manifolds on n vertices, the join of two circles with [n 2] and [n 2] vertices respectively is the unique maximizer of the face numbers. This solves the first case of a conjecture due to Lutz and Nevo. Further, we establish a sharp upper bound on the number of edges of flag 5-manifolds and characterize the cases of equality. We also show that the inequality part of the flag upper bound conjecture continues to hold for all flag 3-dimensional Eulerian complexes and characterize the cases of equality in this class.
Source : ScholeXplorer
IsRelatedTo ARXIV 1202.2810 Source : ScholeXplorer IsRelatedTo DOI 10.1007/s00454-013-9544-7 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.1202.2810
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