Results 321 to 330 of about 2,666,039 (345)
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1998
Plane graphs and their colorings have been the subject of intensive research since the beginnings of graph theory because of their connection to the fourcolor problem. As stated originally the four-color problem asked whether it is always possible to color the regions of a plane map with four colors such that regions which share a common boundary (and ...
Günter M. Ziegler, Martin Aigner
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Plane graphs and their colorings have been the subject of intensive research since the beginnings of graph theory because of their connection to the fourcolor problem. As stated originally the four-color problem asked whether it is always possible to color the regions of a plane map with four colors such that regions which share a common boundary (and ...
Günter M. Ziegler, Martin Aigner
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Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm - SODA '06, 2006
We investigate the number of plane geometric, i.e., straight-line, graphs, a set S of n points in the plane admits. We show that the number of plane graphs and connected plane graphs as well as the number of cycle-free plane graphs is minimized when S is in convex position.
Oswin Aichholzer +5 more
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We investigate the number of plane geometric, i.e., straight-line, graphs, a set S of n points in the plane admits. We show that the number of plane graphs and connected plane graphs as well as the number of cycle-free plane graphs is minimized when S is in convex position.
Oswin Aichholzer +5 more
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Lines in the plane and decompositions of graphs
1998Perhaps the best-known problem on configurations of lines was raised by Sylvester in 1893 in a column of mathematical problems.
Günter M. Ziegler, Martin Aigner
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Plane Graphs and Planar Graphs
2003As we have seen, a graph can be represented graphically, that is, a graph can be drawn in the plane, and it is this kind of graphical presentation that helps us intuitively understand many of structural properties of graphs. In many real-world problems, for example, layout of printed circuits, one wish to draw a graph in the plane such that its edges ...
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1998
Abstract Often it is advantageous to draw graphs. As you can see, most of the graphs in this book are specificed by a picture (instead of a list of vertices and edges, say). But so far we have been studying properties of graphs not related to their drawings, and the role of drawings was purely auxiliary.
Jiří Matoušek, Jaroslav Nešetřil
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Abstract Often it is advantageous to draw graphs. As you can see, most of the graphs in this book are specificed by a picture (instead of a list of vertices and edges, say). But so far we have been studying properties of graphs not related to their drawings, and the role of drawings was purely auxiliary.
Jiří Matoušek, Jaroslav Nešetřil
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Drawing Graphs in the Plane with High Resolution
SIAM Journal on Computing, 1993The authors consider drawings of graphs in the plane such that edges are straight line segments and the minimum angle formed by any pair of incident edges is as large as possible; this maximum is called a resolution of a graph. For any graph with maximum valency \(d\) the resolution \(R\) of the graph satisfies the inequality \(\Omega(d^{-2})\leq R\leq
Formann, M. +7 more
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SIAM Journal on Computing, 1999
Plane graphs \(G\) can be represented by floor plans. A floor plan is a rectangle, partitioned into a set of disjoint rectilinear polygonal regions, which are called the modules. Every module presents a vertex, and it is required that two modules share a piece of their borders if and only if the corresponding vertices are adjacent in \(G\). It has been
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Plane graphs \(G\) can be represented by floor plans. A floor plan is a rectangle, partitioned into a set of disjoint rectilinear polygonal regions, which are called the modules. Every module presents a vertex, and it is required that two modules share a piece of their borders if and only if the corresponding vertices are adjacent in \(G\). It has been
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A note on coverings of plane graphs
Journal of Graph Theory, 1995AbstractFor any plane graph G the number of edges in a minimum edge covering of the faces of G is at most the vertex independence number of G and the numbre of vertices in a minimum vertex covering of the faces of G is at most the edge independence number of G. © 1995 John Wiley & Sons, Inc.
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Who Needs Crossings? Hardness of Plane Graph Rigidity
International Symposium on Computational Geometry, 2016Zachary Abel +5 more
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A method for describing a graph in the plane
Cybernetics, 1986In order to pass from a graph, situated in the plane, to the real topology of a microcircuit, one needs a description of it which guarantees a suitable transformation of information. For this one applies the following methods: enumeration of all faces of the graph or its cycles, fixing of the disposition in a discrete structure, etc.
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