Browsing by Author "Huemer, Clemens"

Note on the number of obtuse angles in point sets
FabilaMonroy, Ruy; Huemer, Clemens; Tramuns, Eulàlia (201409)
Article
Open AccessIn $1979$ Conway, Croft, Erd\H{o}s and Guy proved that every set $S$ of $n$ points in general position in the plane determines at least $\frac{n^3}{18}O(n^2)$ obtuse angles and also presented a special set of $n$ points ... 
On cyclic Kautz digraphs
Böhmová, Katerina; Dalfó Simó, Cristina; Huemer, Clemens (2015)
External research report
Open AccessA prominent problem in Graph Theory is to find extremal graphs or digraphs with restrictions in their diameter, degree and number of vertices. Here we obtain a new family of digraphs with minimal diameter, that is, given ... 
On kgons and kholes in point sets
Aichholzer, Oswin; Fabila Monroy, Ruy; Gonzalez Aguilar, Hernan; Hackl, Thomas; Heredia, Marco A.; Huemer, Clemens; Urrutia Galicia, Jorge; Valtr, Pavel; Vogtenhuber, Birgit (20150801)
Article
Open AccessWe consider a variation of the classical ErdosSzekeres problems on the existence and number of convex kgons and kholes (empty kgons) in a set of n points in the plane. Allowing the kgons to be nonconvex, we show ... 
On some partitioning problems for twocolored point sets
Grima, Clara; Hernando Martín, María del Carmen; Huemer, Clemens; Hurtado Díaz, Fernando Alfredo (2009)
Conference report
Open AccessLet S be a twocolored set of n points in general position in the plane. We show that S admits at least 2 n 17 pairwise disjoint monochromatic triangles with vertices in S and empty of points of S. We further show ... 
On the disks with diameters the sides of a convex 5gon
Huemer, Clemens; PérezLantero, Pablo (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II (MA2), 2015)
Conference report
Restricted access  publisher's policyWe prove that for any convex pentagon there are two disks, among the five disks having a side of the pentagon as diameter and the midpoint of the side as its center, that do not intersect. This shows that K5 is never the ... 
Optimal grid drawings of complete multipartite graphs and an integer variant of the algebraic connectivity
Fabila Monroy, Ruy; Hidalgo Toscano, Carlos; Huemer, Clemens; Lara, Dolores; Mitsche, Dieter (Springer, 2018)
Conference lecture
Restricted access  publisher's policyHow to draw the vertices of a complete multipartite graph G on different points of a bounded ddimensional integer grid, such that the sum of squared distances between vertices of G is (i) minimized or (ii) maximized? For ... 
Order types of random point sets can be realized with small integer coordinates
FabilaMonroy, Ruy; Huemer, Clemens (2017)
Conference report
Open AccessLet S := {p1, . . . , pn} be a set of n points chosen independently and uniformly at random from the unit square and let M be a positive integer. For every point pi = (xi , yi) in S, let p 0 i = (bMxic, bMyic). Let S 0 := ... 
Production matrices for geometric graphs
Huemer, Clemens; Pilz, Alexander; Seara Ojea, Carlos; Silveira, Rodrigo Ignacio (2016)
Article
Open AccessWe present production matrices for noncrossing geometric graphs on point sets in convex position, which allow us to derive formulas for the numbers of such graphs. Several known identities for Catalan numbers, Ballot ... 
Ramsey numbers for empty convex polygons
BautistaSantiago, Crevel; Cano, Javier; FabilaMonroy, Ruy; HidalgoToscano, Carlos; Huemer, Clemens; Leaños, Jesús; Sakai, Toshinori; Urrutia, Jorge (University of Ljubljana, 2015)
Conference report
Restricted access  publisher's policyWe study a geometric Ramsey type problem where the vertices of the complete graph Kn are placed on a set S of n points in general position in the plane, and edges are drawn as straightline segments. We define the empty ... 
Recoloring directed graphs
Felsner, Stefan; Huemer, Clemens; Saumell Mendiola, Maria (Prensas Universitarias de Zaragoza, 2009)
Conference report
Open AccessLet G be a directed graph and k a positive integer. We define the kcolor graph of G (Dk(G) for short) as the directed graph having all kcolorings of G as node set, and where two kcolorings and ' are joined by a ... 
The connectivity of the flip graph of Hamiltonian paths of the grid graph
Duque, Frank; Fabila Monroy, Ruy; Flores Peñazola, David; Hidalgo Toscano, Carlos; Huemer, Clemens (2017)
Conference report
Open AccessLet Gn,m be the grid graph with n columns and m rows. Let Hn,m be the graph whose vertices are the Hamiltonian paths in Gn,m, where two vertices P1 and P2 are adjacent if we can obtain P2 from P1 by deleting an edge in P1 ... 
The degreediameter problem in maximal bipartite planar graphs
Dalfó Simó, Cristina; Huemer, Clemens; Salas, Julian (2014)
Conference lecture
Open AccessThe (A ,D) (degree/diameter) problem consists of finding the largest possible number of vertices n among all the graphs with maximum degree and diameter D. We consider the (A ,D) problem for maximal planar bipartite ... 
The degree/diameter problem in maximal planar bipartite graphs
Dalfó Simó, Cristina; Huemer, Clemens; Salas Piñon, Julián (2014)
Article
Open AccessThe (¿;D) (degree/diameter) problem consists of nding the largest possible number of vertices n among all the graphs with maximum degree ¿ and diameter D. We consider the (¿;D) problem for maximal planar bipartite graphs, ... 
The degree/diameter problem in maximal planar bipartite graphs
Dalfó Simó, Cristina; Huemer, Clemens; Salas Piñon, Julián (2016)
Article
Open AccessThe (Δ,D)(Δ,D) (degree/diameter) problem consists of finding the largest possible number of vertices nn among all the graphs with maximum degree ΔΔ and diameter DD. We consider the (Δ,D)(Δ,D) problem for maximal planar ... 
The diameter of cyclic Kautz digraphs
Böhmová, Katerina; Dalfó Simó, Cristina; Huemer, Clemens (20151112)
Article
Open AccessA prominent problem in Graph Theory is to find extremal graphs or digraphs with restrictions in their diameter, degree and number of vertices. Here we obtain a new family of digraphs with minimal diameter, that is, given ... 
The diameter of cyclic Kautz digraphs
Böhmová, Katerina; Dalfó Simó, Cristina; Huemer, Clemens (2017)
Article
Open AccessWe present a new kind of digraphs, called cyclic Kautz digraphs CK(d, `), which are subdigraphs of the wellknown Kautz digraphs K(d, `). The latter have the smallest diameter among all digraphs with their number of vertices ... 
The number of empty fourgons in random point sets
FabilaMonroy, Ruy; Huemer, Clemens; Mitsche, Dieter (2014)
Article
Open AccessLet S be a set of n points distributed uniformly and independently in the unit square. Then the expected number of empty fourgons with vertices from S is T(n^2 log¿ n). A fourgon is empty if it contains no points of S ... 
The rotation graph of kary trees is Hamiltonian
Huemer, Clemens; Hurtado Díaz, Fernando Alfredo; Pfeifle, Julián (Crete University Press, 2006)
Article
Restricted access  publisher's policyIn this paper we show that the graph of kary trees, connected by rotations, contains a Hamilton cycle. Our proof is constructive and thus provides a cyclic Gray code for kary trees. Furthermore, we identify a basic ...