Zobrazeno 1 - 10
of 464
pro vyhledávání: '"52c99"'
Autor:
Clifton, Alexander, Simon, Dániel G.
We investigate two notions of saturation for partial planar embeddings of maximal planar graphs. Let $G = (V, E) $ be a vertex-labeled maximal planar graph on $ n $ vertices, which by definition has $3n - 6$ edges. We say that a labeled plane graph $
Externí odkaz:
http://arxiv.org/abs/2412.06068
Autor:
Almog, Yaniv
We study the pair interaction on flat tori of functions whose Fourier coefficients are positive and decay sufficiently rapidly. In dimension one we find that the minimizer, up to translation, is the equidistant point set. In dimension two, minimizing
Externí odkaz:
http://arxiv.org/abs/2412.03425
A set of n non-collinear points in the Euclidean plane defines at least n different lines. Chen and Chv\'tal in 2008 conjectured that the same results is true in metric spaces for an adequate definition of line. More recently, it was conjectured in 2
Externí odkaz:
http://arxiv.org/abs/2410.21433
Autor:
Ranđelović, Žarko
Given functions $f,g: [n] \rightarrow [n]$ do there exist $n$ points $A_1,A_2\ldots A_n$ in some metric space such that $A_{f(i)},A_{g(i)}$ are the points closest and farthest from point $A_i$? In this paper we characterize precisely which pairs of f
Externí odkaz:
http://arxiv.org/abs/2409.14648
We explore properties of generalized Paley graphs and we extend a result of Lim and Praeger by providing a more precise description of the connected components of disconnected generalized Paley graphs. This result leads to a new characterization of w
Externí odkaz:
http://arxiv.org/abs/2409.03631
Autor:
MIT CompGeom Group, Akitaya, Hugo A., Demaine, Erik D., Hesterberg, Adam, Lubiw, Anna, Lynch, Jayson, O'Rourke, Joseph, Stock, Frederick, Tkadlec, Josef
A polyiamond is a polygon composed of unit equilateral triangles, and a generalized deltahedron is a convex polyhedron whose every face is a convex polyiamond. We study a variant where one face may be an exception. For a convex polygon P, if there is
Externí odkaz:
http://arxiv.org/abs/2408.04687
Autor:
MIT CompGeom Group, Akitaya, Hugo A., Demaine, Erik D., Hesterberg, Adam, Lubiw, Anna, Lynch, Jayson, O'Rourke, Joseph, Stock, Frederick
We explore an Art Gallery variant where each point of a polygon must be seen by k guards, and guards cannot see through other guards. Surprisingly, even covering convex polygons under this variant is not straightforward. For example, covering every p
Externí odkaz:
http://arxiv.org/abs/2404.04613
Autor:
Keil, J. Mark, Mondal, Debajyoti
A disk graph is an intersection graph of disks in $\mathbb{R}^2$. Determining the computational complexity of finding a maximum clique in a disk graph is a long-standing open problem. In 1990, Clark, Colbourn, and Johnson gave a polynomial-time algor
Externí odkaz:
http://arxiv.org/abs/2404.03751
Autor:
Kiss, Gergely, Laczkovich, Miklós
Let $K$ be a nonempty finite subset of the Euclidean space $\mathbb{R}^k$ $(k\ge 2)$. We prove that if a function $f\colon \mathbb{R}^k\to \mathbb{C}$ is such that the sum of $f$ on every congruent copy of $K$ is zero, then $f$ vanishes everywhere. I
Externí odkaz:
http://arxiv.org/abs/2403.01279
Autor:
Führer, Jakob, Tóth, Géza
Conlon and Wu showed that there is a red/blue-coloring of $\mathbb{E}^n$ that does not contain $3$ red collinear points separated by unit distance and $m=10^{50}$ blue collinear points separated by unit distance. We prove that the statement holds wit
Externí odkaz:
http://arxiv.org/abs/2402.12567