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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 ...
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Plane Graphs with Acyclic Complex

2001
All vertex-sets of cliques of G form the simplexes of an abstract complex C(G), which is called the clique complex of G. It is proved that the clique complex of a plane graph G is acyclic if and only if G is contractible.
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A note on coverings of plane graphs

Journal of Graph Theory, 1995
AbstractFor 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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Plane triangulations in product graphs.

Ars Comb., 2004
Summary: A graph \(G\) is said to be locally Hamiltonian if the subgraph induced by the neighbourhood of every vertex is Hamiltonian. \textit{M. Alabdullatif} [Bull. Inst. Comb. Appl. 30, 91--100 (2000; Zbl 0966.05046)] conjectured that every connected locally Hamiltonian graph contains a spanning plane triangulation. We disprove the conjecture. At the
P. Paulraja, N. Varadarajan
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On the number of plane graphs

Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm - SODA '06, 2006
Oswin Aichholzer   +5 more
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An exact cutting plane algorithm to solve the selective graph coloring problem in perfect graphs

European Journal of Operational Research, 2021
Tinaz Ekim   +2 more
exaly  

Graph theory implementation in plane frame analysis

International Journal of Structural Engineering, 2023
Rajkumar Raikar
exaly  

FLOWER AS A MAGIC PLANE GRAPH

Advances and Applications in Discrete Mathematics, 2020
Ashkenazi, Yehuda, Busharyan, Ruth
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