Lech Duraj,Ross J Kang,Hoang La et al.
Lech Duraj et al.
Given a positive integer d, the class d-DIR is defined as all those intersection graphs formed from a finite collection of line segments in R 2 having at most d slopes. Since each slope induces an interval graph, it easily follows for eve...
Agelos Georgakopoulos
Agelos Georgakopoulos
Mohar recently adapted the classical game of Cops and Robber from graphs to metric spaces, thereby unifying previously studied pursuit-evasion games. He conjectured that finitely many cops can win on any compact geodesic metric space, and t...
Nóra Frankl,Panna Gehér,Arsenii Sagdeev et al.
Nóra Frankl et al.
We prove that for any ℓ p -norm in the plane with 1
Joseph Doolittle,Alex McDonough
Joseph Doolittle
It is broadly known that any parallelepiped tiles space by translating copies of itself along its edges. In earlier work relating to higher-dimensional sandpile groups, the second author discovered a novel construction which fragments the p...
Cesar Ceballos,Joseph Doolittle
Cesar Ceballos
A famous theorem in polytope theory states that the combinatorial type of a simplicial polytope is completely determined by its facet-ridge graph. This celebrated result was proven by Blind and Mani (Aequationes Math 34(2-3):287-297, 1987, ...
Anthony Nixon,Bernd Schulze,Joseph Wall
Anthony Nixon
A bar-joint framework (G, p) is the combination of a finite simple graph G = ( V , E ) and a placement p : V → R d . The framework is rigid if the only edge-length preserving continuous motions of the vertices arise from isometries...
Peeling Sequences [0.03%]
剥皮序列问题
Adrian Dumitrescu,Géza Tóth
Adrian Dumitrescu
Given a set of n labeled points in general position in the plane, we remove all of its points one by one. At each step, one point from the convex hull of the remaining set is erased. In how many ways can the process be carried out? The answ...
Herbert Edelsbrunner,Anton Nikitenko
Herbert Edelsbrunner
The approximation of a circle with the edges of a fine square grid distorts the perimeter by a factor about 4 π . We prove that this factor is the same on average (in the ergodic sense) for approximations of any rectifiable curve by...
On Angles in Higher Order Brillouin Tessellations and Related Tilings in the Plane [0.03%]
论平面高阶布里渊镶嵌及相关铺砌中的角度问题
Herbert Edelsbrunner,Alexey Garber,Mohadese Ghafari et al.
Herbert Edelsbrunner et al.
For a locally finite set in R 2 , the order-k Brillouin tessellations form an infinite sequence of convex face-to-face tilings of the plane. If the set is coarsely dense and generic, then the corresponding infinite sequences of minimum an...
Deep Cliques in Point Sets [0.03%]
点集中的深团簇
Stefan Langerman,Marcelo Mydlarz,Emo Welzl
Stefan Langerman
Let n ∈ N and k ∈ N 0 . Given a set P of n points in the plane, a pair { p , q } of points in P is called k-deep, if there are at least k points from P strictly on each side of the line spanned by p and q. A k-deep clique is...