Homothetic Triangle Contact Representations of Planar Graphs
نویسندگان
چکیده
In this paper we study the problem of computing homothetic triangle contact representations of planar graphs. Since not all planar graphs admit such a representation, we concentrate on meaningful subfamilies of planar graphs and prove that: (i) every two-terminal seriesparallel digraph has a homothetic triangle contact representation, which can be computed in linear time; (ii) every partial planar 3-tree admits a homothetic triangle contact representation.
منابع مشابه
Equilateral L-Contact Graphs
We consider L-graphs, that is contact graphs of axis-aligned L-shapes in the plane, all with the same rotation. We provide several characterizations of Lgraphs, drawing connections to Schnyder realizers and canonical orders of maximally planar graphs. We show that every contact system of L’s can always be converted to an equivalent one with equilateral L’s. This can be used to show a stronger v...
متن کاملPentagon Contact Representations
Representations of planar triangulations as contact graphs of a set of internally disjoint homothetic triangles or respectively of a set of internally disjoint homothetic squares have received quite some attention in recent years. In this paper we investigate representations of planar triangulations as contact graphs of a set of internally disjoint homothetic pentagons. Surprisingly such a repr...
متن کاملTouching Triangle Representations for 3-Connected Planar Graphs
A touching triangle graph (TTG) representation of a planar graph is a planar drawing Γ of the graph, where each vertex is represented as a triangle and each edge e is represented as a side contact of the triangles that correspond to the end vertices of e. We call Γ a proper TTG representation if Γ determines a tiling of a triangle, where each tile corresponds to a distinct vertex of the input g...
متن کاملSquare-Contact Representations of Partial 2-Trees and Triconnected Simply-Nested Graphs
A square-contact representation of a planar graph G = (V,E) maps vertices in V to interiordisjoint axis-aligned squares in the plane and edges in E to adjacencies between the sides of the corresponding squares. In this paper, we study proper square-contact representations of planar graphs, in which any two squares are either disjoint or share infinitely many points. We characterize the partial ...
متن کاملStraight Line Triangle Representations
A straight line triangle representation (SLTR) of a planar graph is a straight line drawing such that all the faces including the outer face have triangular shape. Such a drawing can be viewed as a tiling of a triangle using triangles with the input graph as skeletal structure. In this paper we present a characterization of graphs that have an SLTR. The charcterization is based on flat angle as...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007