Now showing items 1-8 of 8

    • A new upper bound for 3-SAT 

      Díaz Cort, Josep; Lefteris, Kirousis; Mitsche, Dieter; Perez-Gimenez, Xavier (Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany, 2008)
      Conference report
      Open Access
      We show that a randomly chosen 3-CNF formula over n variables with clauses-tovariables ratio at least 4.4898 is asymptotically almost surely unsatisfiable. The previous best such bound, due to Dubois in 1999, was 4.506. ...
    • Corrigendum to"On the limiting distribution of the metric dimension for random forests" [European J. Combin. 49 (2015) 68-89] 

      Mitsche, Dieter; Rué Perna, Juan José (2017-07-22)
      Article
      Open Access
      In the paper ”On the limiting distribution of the metric dimension for random forests” the metric dimension ß(G) of sparse G(n, p) with p = c/n and c < 1 was studied (Theorem 1.2). In the proof of this theorem, for the ...
    • Empty non-convex and convex four-gons in random point sets 

      Fabila Monroy, Ruy; Huemer, Clemens; Mitsche, Dieter (2015-03-01)
      Article
      Open Access
      Let S be a set of n points distributed uniformly and independently in a convex, bounded set in the plane. A four-gon is called empty if it contains no points of S in its interior. We show that the expected number of empty ...
    • Learning random points from geometric graphs or orderings 

      Díaz Cort, Josep; Mcdiarmid, Colin; Mitsche, Dieter (2020-09)
      Article
      Restricted access - publisher's policy
      Let Xv for v∈V be a family of n iid uniform points in the square (Formula presented.). Suppose first that we are given the random geometric graph (Formula presented.), where vertices u and v are adjacent when the Euclidean ...
    • On the limiting distribution of the metric dimension for random forests 

      Rué Perna, Juan José; Mitsche, Dieter (2015-03-20)
      Article
      Open Access
      The metric dimension of a graph G is the minimum size of a subset S of vertices of G such that all other vertices are uniquely determined by their distances to the vertices in S. In this paper we investigate the metric ...
    • On the treewidth and related parameters of random geometric graphs 

      Mitsche, Dieter; Perarnau Llobet, Guillem (2017-06-22)
      Article
      Restricted access - publisher's policy
      We give asymptotically exact values for the treewidth tw(G) of a random geometric graph G ¿ G(n, r) in [0, v n] 2 . More precisely, let rc denote the threshold radius for the appearance of the giant component in G(n, r). ...
    • 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 policy
      How to draw the vertices of a complete multipartite graph G on different points of a bounded d-dimensional integer grid, such that the sum of squared distances between vertices of G is (i) minimized or (ii) maximized? For ...
    • The number of empty four-gons in random point sets 

      Fabila-Monroy, Ruy; Huemer, Clemens; Mitsche, Dieter (2014)
      Article
      Open Access
      Let S be a set of n points distributed uniformly and independently in the unit square. Then the expected number of empty four-gons with vertices from S is T(n^2 log¿ n). A four-gon is empty if it contains no points of S ...