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The maximum diameter of pure simplicial complexes and pseudo-manifolds

Abstract: We construct d-dimensional pure simplicial complexes and pseudo-manifolds (without boundary) with n vertices whose combinatorial diameter grows as cdnd - 1 for a constant cd depending only on d, which is the maximum possible growth. Moreover, the constant cd is optimal modulo a singly exponential factor in d. The pure simplicial complexes improve on a construction of the second author that achieved cdn2 d / 3. For pseudo-manifolds without boundary, as far as we know, no construction with diameter greater than n2 was previously known.

 Fuente: Discrete and Computational Geometry, 2017, 58(3), 643-649

 Editorial: Springer New York LLC

 Fecha de publicación: 01/10/2017

 Nº de páginas: 7

 Tipo de publicación: Artículo de Revista

 DOI: 10.1007/s00454-017-9888-5

 ISSN: 0179-5376,1432-0444

 Proyecto español: MTM2014-54207-P

 Url de la publicación: https://doi.org/10.1007/s00454-017-9888-5

Autoría

FRANCISCO CRIADO GALLART