On L-shaped point set embeddings of trees: first non-embeddable examples
نویسندگان
چکیده
منابع مشابه
Planar L - Shaped Point Set Embeddings of Trees ∗
In this paper we consider planar L-shaped embeddings of trees in point sets, that is, planar drawings where the vertices are mapped to a subset of the given points and where every edge consists of two axis-aligned line segments. We investigate the minimum number m, such that any n vertex tree with maximum degree 4 admits a planar L-shaped embedding in any point set of size m. First we give an u...
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A straight-line drawing of a plane graph G is a planar drawing of G, where each vertex is drawn as a point and each edge is drawn as a straight line segment. Given a set S of n points in the Euclidean plane, a point-set embedding of a plane graph G with n vertices on S is a straight-line drawing of G, where each vertex of G is mapped to a distinct point of S. The problem of deciding if G admits...
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A straight-line drawing of a plane graph G is a planar drawing of G, where each vertex is drawn as a point and each edge is drawn as a straight-line segment. Given a set S of n points on the Euclidean plane, a point-set embedding of a plane graph G with n vertices on S is a straight-line drawing of G, where each vertex of G is mapped to a distinct point of S. The problem of deciding if G admits...
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In an orthogeodesic embedding of a graph, each edge is embedded as an axis-parallel polyline that forms a shortest path in the `1 metric. In this paper we consider orthogeodesic plane embeddings of trees on grids. A grid is implicitly defined by a set P ⊂ R of points. Denote by ΓP the arrangement induced by all horizontal and vertical lines that pass through a point from P . When embedding a gr...
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We show that any planar drawing of a forest of three stars whose vertices are constrained to be at fixed vertex locations may require Ω(n 2 3 ) edges each having Ω(n 1 3 ) bends in the worst case. The lower bound holds even when the function that maps vertices to points is not a bijection but it is defined by a 3-coloring. In contrast, a constant number of bends per edge can be obtained for 3-c...
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ژورنال
عنوان ژورنال: Journal of Graph Algorithms and Applications
سال: 2020
ISSN: 1526-1719
DOI: 10.7155/jgaa.00537