Results 251 to 260 of about 2,427,282 (299)

Facial Colorings of Plane Graphs

J. Interconnect. Networks, 2019
This paper extends and updates the survey [J. Czap, S. Jendrol’, Facially-constrained colorings of plane graphs: A survey, Discrete Math. 340 (2017) 2691–2703] on facial colorings.
J. Czap, S. Jendrol’
semanticscholar   +1 more source

The Odd-Distance Plane Graph

Discrete & Computational Geometry, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ardal, Hayri, Maňuch, Ján, Rosenfeld, Moshe, Shelah, Saharon, Stacho, Ladislav   +4 more
openaire   +2 more sources

Nonconvex Representations of Plane Graphs

SIAM Journal on Discrete Mathematics, 2012
We 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, FRATI, FABRIZIO, PATRIGNANI, Maurizio   +2 more
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Drawing plane graphs nicely

Acta Informatica, 1985
This paper presents two efficient algorithms for drawing plane graphs nicely. Both draw all edges of a graph as straight line segments without crossing lines. The first draws a plane graph ''convex'' if possible, that is, in a way that every inner face and the complement of the outer face are convex polygons.
Chiba, Norishige, Onoguchi, Kazunori, Nishizeki, Takao   +2 more
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Characterizing the computational power of mobile robots on graphs and implications for the Euclidean plane

Information and Computation, 2018
In this paper we study the computational power of mobile robots without global coordination. A comprehensive evaluation of the computational power of robots moving within the Euclidean plane has been proposed by Das et al. in 2016.
Mattia D’emidio, G. Stefano, D. Frigioni, A. Navarra   +3 more
semanticscholar   +1 more source

Plane Graphs and Planar Graphs

2003
As 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 ...
openaire   +1 more source

INNER RECTANGULAR DRAWINGS OF PLANE GRAPHS

International Journal of Computational Geometry & Applications, 2006
A drawing of a plane graph is called an inner rectangular drawing if every edge is drawn as a horizontal or vertical line segment so that every inner face is a rectangle. In this paper we show that a plane graph G has an inner rectangular drawing D if and only if a new bipartite graph constructed from G has a perfect matching.
Miura, Kazuyuki, Haga, Hiroki, Nishizeki, Takao   +2 more
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On the Facial Thue Choice Number of Plane Graphs Via Entropy Compression Method

Graphs Comb., 2013
Let G be a plane graph. A vertex-colouring $$\varphi $$φ of G is called facial non-repetitive if for no sequence $$r_1 r_2 \ldots r_{2n}$$r1r2…r2n, $$n\ge 1$$n≥1, of consecutive vertex colours of any facial path it holds $$r_i=r_{n+i}$$ri=rn+i for all ...
J. Przybylo, Jens Schreyer, E. Škrabul'áková   +2 more
semanticscholar   +1 more source

Drawing Plane Graphs

2003
Automatic aesthetic drawing of plane graphs has recently created intense interest due to its broad applications, and as a consequence, a number of drawing methods, such as the straight line drawing, convex drawing, orthogonal drawing, rectangular drawing and box-rectangular drawing, have come out [8,9,3,4,5,6,7, 10,11,14,16,23,29,33].
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Five-coloring plane graphs

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 ...
Martin Aigner, Günter M. Ziegler
openaire   +1 more source