Proximity Drawings
نویسنده
چکیده
University of Perugia 4.
منابع مشابه
Approximate Proximity Drawings
We introduce and study a generalization of the well-known region of influence proximity drawings, called (ε1, ε2)-proximity drawings. Intuitively, given a definition of proximity and two real numbers ε1 ≥ 0 and ε2 ≥ 0, an (ε1, ε2)-proximity drawing of a graph is a planar straight-line drawing Γ such that: (i) for every pair of adjacent vertices u, v, their proximity region “shrunk” by the multi...
متن کاملProximity Drawings of Outerplanar Graphs ( Preliminary
A proximity drawing of a graph is one in which pairs of adjacent vertices are drawn relatively close together according to some proximity measure while pairs of non-adjacent vertices are drawn relatively far apart. The fundamental question concerning proximity drawability is: Given a graph G and a deenition of proximity, is it possible to construct a proximity drawing of G? We consider this que...
متن کاملProximity Drawings of Outerplanar Graphs
A proximity drawing of a graph is one in which pairs of adjacent vertices are relatively close together according to some proximity measure, while pairs of non-adjacent vertices are relatively far apart. It is the choice of the proximity measure that determines the type of proximity drawing. Although proximity drawings have many uses, the study of their combinatorial properties is still in its ...
متن کاملThe Strength of Weak Proximity ? ( extended
This paper initiates the study of weak proximity drawings of graphs and demonstrates their advantages over strong proximity drawings in certain cases. Weak proximity drawings are straight line drawings such that if the proximity region of two points p and q representing ver-tices is devoid of other points representing vertices, then segment (p; q) is allowed, but not forced, to appear in the dr...
متن کاملOn Vertex- and Empty-Ply Proximity Drawings
We initiate the study of the vertex-ply of straight-line drawings, as a relaxation of the recently introduced ply number. Consider the disks centered at each vertex with radius equal to half the length of the longest edge incident to the vertex. The vertex-ply of a drawing is determined by the vertex covered by the maximum number of disks. The main motivation for considering this relaxation is ...
متن کاملArea Requirement of Gabriel Drawings ? (extended Abstract)
In this paper we investigate the area requirement of proximity drawings and we prove an exponential lower bound. Our main contribution is to show the existence of a class of Gabriel-drawable graphs that require exponential area for any Gabriel drawing and any resolution rule. The result is further extended to an innnite class of proximity drawings.
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