T-shape visibility representations of 1-planar graphs

نویسنده

  • Franz-Josef Brandenburg
چکیده

A shape visibility representation displays a graph so that each vertex is represented by an orthogonal polygon of a particular shape and for each edge there is a horizontal or vertical line of sight between the polygons assigned to its endvertices. Special shapes are rectangles, L, T, E and H-shapes, and caterpillars. A flat rectangle is a horizontal bar of height > 0. A graph is 1-planar if there is a drawing in the plane such that each edge is crossed at most once and is IC-planar if in addition no two crossing edges share a vertex. We show that every IC-planar graph has a flat rectangle visibility representation and that every 1-planar graph has a T-shape visibility representation. The representations use quadratic area and can be computed in linear time from a given embedding.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

1-Visibility Representations of 1-Planar Graphs

A visibility representation is a classical drawing style of planar graphs. It displays the vertices of a graph as horizontal vertexsegments, and each edge is represented by a vertical edge-segment touching the segments of its end vertices; beyond that segments do not intersect. We generalize visibility to 1-visibility, where each edge(vertex-) segment crosses at most one vertex(edge-) segment. ...

متن کامل

A More Compact Visibility Representation

16 4-block tree in linear time. The problem is already linear time solvable in case of 2-and 3-connected components (see e.g., Hopcroft & Tarjan 8]), hence solving this open problem yields a nice generalization. As a last subject we consider the method of triangulating planar graphs. It would be interesting to triangulate G such that it is 4-connected. Indeed, G may have separating triangles, i...

متن کامل

Bar k-Visibility Graphs: Bounds on the Number of Edges, Chromatic Number, and Thickness

Let S be a set of horizontal line segments, or bars, in the plane. We say that G is a bar visibility graph, and S its bar visibility representation, if there exists a one-to-one correspondence between vertices of G and bars in S, such that there is an edge between two vertices in G if and only if there exists an unobstructed vertical line of sight between their corresponding bars. If bars are a...

متن کامل

3D Visibility Representations of 1-planar Graphs

We prove that every 1-planar graph G has a z-parallel visibility representation, i.e., a 3D visibility representation in which the vertices are isothetic disjoint rectangles parallel to the xy-plane, and the edges are unobstructed z-parallel visibilities between pairs of rectangles. In addition, the constructed representation is such that there is a plane that intersects all the rectangles, and...

متن کامل

Bar k-Visibility Graphs

Let S be a set of horizontal line segments, or bars, in the plane. We say that G is a bar visibility graph, and S its bar visibility representation, if there exists a one-to-one correspondence between vertices of G and bars in S, such that there is an edge between two vertices in G if and only if there exists an unobstructed vertical line of sight between their corresponding bars. If bars are a...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Comput. Geom.

دوره 69  شماره 

صفحات  -

تاریخ انتشار 2018