2015/12/16 by Salman Parsa, Parsa, Salman
Computer Science · #Topological and Geometric Data Analysis #Advanced Graph Theory Research #Graph Labeling and Dimension Problems
paper · pdf · doi:10.48550/arxiv.1512.05164
We consider d-dimensional simplicial complexes which can be PL embedded in\nthe 2d-dimensional euclidean space. In short, we show that in any such\ncomplex, for any three vertices, the intersection of the link-complexes of the\nvertices is linklessly embeddable in the (2d-1)-dimensional euclidean space.\nThese considerations lead us to a new upper bound on the total number of\nd-simplices in an embeddable complex in 2d-space with n vertices,\nimproving known upper bounds, for all d \≥ 2. Moreover, the bound is also\ntrue for the size of d-complexes linklessly embeddable in the\n(2d+1)-dimensional space.\n