Drawing cubic graphs with at most five slopes
نویسندگان
چکیده
منابع مشابه
Drawing Cubic Graphs with at Most Five Slopes
We show that every graph G with maximum degree three has a straight-line drawing in the plane using edges of at most five different slopes. Moreover, if G is connected and has at least one vertex of degree less than three, then four directions suffice.
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We show that every cubic graph can be drawn in the plane with straight-line edges using only the four basic slopes {0, π/4, π/2, 3π/4}. We also prove that four slopes have this property if and only if we can draw K4 with them.
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Let G be a connected simple cubic graph; Aut G denotes its automorphism group. Let n be half the number of vertices of G. We define the arithmetic genus of a (possibly disconnected) graph as e−v+1 where e is the number of edges, v the number of vertices of G). For a connected simple cubic graph, g = n+1. The definition of arithmetic genus is motivated by the following: to a projective nodal cur...
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We settle a problem of Dujmović, Eppstein, Suderman, and Wood by showing that there exists a function f with the property that every planar graph G with maximum degree d admits a drawing with noncrossing straight-line edges, using at most f(d) different slopes. If we allow the edges to be represented by polygonal paths with one bend, then 2d slopes suffice. Allowing two bends per edge, every pl...
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A graph is outer 1-planar if it admits a drawing where each vertex is on the outer face and each edge is crossed by at most another edge. Outer 1-planar graphs are a superclass of the outerplanar graphs and a subclass of the planar partial 3-trees. We show that an outer 1-planar graph G of bounded degree ∆ admits an outer 1-planar straight-line drawing that uses O(∆) different slopes, which gen...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2008
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2007.05.003