Area-efficient planar straight-line drawings of outerplanar graphs
نویسندگان
چکیده
منابع مشابه
Straight-line Drawings of 1-planar Graphs
The classical Fáry’s theorem from the 1930s states that every planar graph can be drawn as a straight-line drawing. In this paper, we extend Fáry’s theorem to non-planar graphs. More specifically, we study the problem of drawing 1-planar graphs with straight-line edges. A 1-planar graph is a sparse non-planar graph with at most one crossing per edge. We give a characterisation of those 1planar ...
متن کاملStraight-line Drawings of Outerplanar Graphs in O(dn log n) Area
We show an algorithm for constructing O(dn log n) area outerplanar straight-line drawings of n-vertex outerplanar graphs with degree d. Also, we settle in the negative a conjecture [1] on the area requirement of outerplanar graphs by showing that snowflake graphs admit linear area drawings.
متن کاملStraight-Line Grid Drawings of Label-Constrained Outerplanar Graphs with O(n log n) Area
A straight-line grid drawing of a planar graph G is a drawing of G on an integer grid such that each vertex is drawn as a grid point and each edge is drawn as a straight-line segment without edge crossings. Any outerplanar graph of n vertices with maximum degree d has a straight-line grid drawing with area O(dn log n). In this paper, we introduce a subclass of outerplanar graphs, which we call ...
متن کاملStraight-Line Grid Drawings of 3-Connected 1-Planar Graphs
A graph is 1-planar if it can be drawn in the plane such that each edge is crossed at most once. In general, 1-planar graphs do not admit straightline drawings. We show that every 3-connected 1-planar graph has a straight-line drawing on an integer grid of quadratic size, with the exception of a single edge on the outer face that has one bend. The drawing can be computed in linear time from any...
متن کاملGA for straight-line grid drawings of maximal planar graphs
osting by E Abstract A straight-line grid drawing of a planar graph G of n vertices is a drawing of G on an integer grid such that each vertex is drawn as a grid point and each edge is drawn as a straight-line segment without edge crossings. Finding algorithms for straight-line grid drawings of maximal planar graphs (MPGs) in the minimum area is still an elusive goal. In this paper we explore t...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2007
ISSN: 0166-218X
DOI: 10.1016/j.dam.2005.12.008