6,892 research outputs found
Fast domino tileability
Domino tileability is a classical problem in Discrete Geometry, famously
solved by Thurston for simply connected regions in nearly linear time in the
area. In this paper, we improve upon Thurston's height function approach to a
nearly linear time in the perimeter.Comment: Appeared in Discrete Comput. Geom. 56 (2016), 377-39
Dense flag triangulations of 3-manifolds via extremal graph theory
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.Comment: Trans. AMS, to appea
Дорожні чеки в господарському обороті України
In this paper we verify a conjecture by Kozlov [D.N. Kozlov, Convex Hulls of f- and beta-vectors, Discrete Comput. Geom. 18 (1997) 421-431], which describes the convex hull of the set of face vectors of r-colorable complexes on n vertices. As part of the proof we derive a generalization of Turn's graph theorem.QC 20140514</p
Algebraic construction of a coboundary of a given cycle
We present an algebraic construction of the coboundary of a given cycle as a simpler alternative to the geometric one introduced in [M. Allili, T. Kaczyński, Geometric construction of a coboundary of a cycle, Discrete Comput. Geom. 25 (2001), 125–140, T. Kaczyński, Recursive coboundary formula for cycles in acyclic chain complexes, Topol. Methods Nonlinear Anal. 18 (2001), 351–371]
Every Large Point Set contains Many Collinear Points or an Empty Pentagon
We prove the following generalised empty pentagon theorem: for every integer
, every sufficiently large set of points in the plane contains
collinear points or an empty pentagon. As an application, we settle the
next open case of the "big line or big clique" conjecture of K\'ara, P\'or, and
Wood [\emph{Discrete Comput. Geom.} 34(3):497--506, 2005]
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