Construction of planar triangulations with minimum degree 5
نویسندگان
چکیده
منابع مشابه
Construction of planar triangulations with minimum degree 5
In this article we describe a method of constructing all simple triangulations of the sphere with minimum degree 5; equivalently, 3-connected planar cubic graphs with girth 5. We also present the results of a computer program based on this algorithm, including counts of convex polytopes of minimum degree 5.
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The classic problem of nding a minimum-weight triangulation for a given planar straight-line graph is considered in this paper. A brief overview of known methods is given in addition to some new results. A parallel greedy triangulation algorithm is presented along with experimental data that suggest a logarithmic relationship between the number of input vertices and its running time in the aver...
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The weight of a path in a graph is defined to be the sum of degrees of its vertices in entire graph. It is proved that each plane triangulation of minimum degree 5 contains a path P5 on 5 vertices of weight at most 29, the bound being precise, and each plane triangulation of minimum degree 4 contains a path P4 on 4 vertices of weight at most 31.
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A connected graph H is said to be light in the family of graphsH if there exists a positive integer k such that each graphG ∈ H that contains an isomorphic copy of H contains a subgraph K isomorphic to H that satisfies the inequality ∑ v∈V (K) degG(v) k. It is known that an r-cycle Cr is light in the family of planar graphs with minimum degree 5 if 3 r 6, and not light for r 11. We prove that C...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2005
ISSN: 0012-365X
DOI: 10.1016/j.disc.2005.06.019