DENSE FLAG TRIANGULATIONS OF 3-MANIFOLDS VIA EXTREMAL GRAPH THEORY

作者：Adamaszek Michal^*; Hladky Jan

来源：Transactions of the American Mathematical Society, 2015, 367(4): 2743-2764.

• f-vector
• simplicial complex
• Gal's conjecture
• flag triangulations of 3-manifolds

We characterize f-vectors of sufficiently large three-dimensional flag Gorenstein* complexes, essentially confirming a conjecture of Gal [Discrete Comput. Geom., 34 (2), 269-284, 2005]. In particular, this characterizes f-vectors of large flag triangulations of the 3-sphere. Actually, our main result is more general and describes the structure of closed flag 3-manifolds which have many edges.
Looking at the 1-skeleta of these manifolds we reduce the problem to a certain question in extremal graph theory. We then resolve this question by employing the Supersaturation Theorem of Erdos and Simonovits.

• 出版日期2015-4