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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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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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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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Embedding Plane Graphs in the Grids
Ninth International Conference on Information Visualisation (IV'05), 2006We have given necessary and sufficient conditions which is an extention of Thomassen's characterization of the rectangular drawing of plane graphs with maximum vertex degree four. A drawing algorithm is also proposed.
Cahit, I., Kheddouci, H.
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Entire Labeling of Plane Graphs
Applied Mathematics & Information Sciences, 2015A face irregular entire k-labeling ϕ : V ( E( F ! f 1, 2,..., kg of a 2-connected plane graph G= (V, E, F) is a labeling of vertices, edges and faces of G in such a way that for any two different faces f and g their weights wϕ( f) and wϕ(g) are distinct.
Kadarkarai Muthugurupackiam +3 more
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Nonconvex Representations of Plane Graphs
SIAM Journal on Discrete Mathematics, 2012We show that every plane graph admits a planar straight-line drawing in which all faces with more than three vertices are nonconvex polygons.
DI BATTISTA, Giuseppe +2 more
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