# planar graph

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## planar graph

[′plā·nər ‚graf]
(mathematics)
A graph that can be drawn in a plane without any lines crossing.
References in periodicals archive ?
The current best algorithm for 4-coloring an m-vertex planar graph runs in O([m.
In particular, one well-known result of Schnyder states that every planar graph has arboricity at most 3, see .
Corresponding to every connected link diagram we can find a connected signed planar graph and vice versa.
In a maximal planar graph G = ((V (G), E(G)) with [absolute value of V (G)]=n and [absolute value of E (G)]=m, we have m = 3n - 6.
There's an interactive planar graph as well that can be rotated with your mouse.
This graph is still too complex to be displayed with reasonably true distances and without crossing lines, so I removed the link between difficult and heavy to obtain at least an approximately planar graph.
Yannakakis has investigated the book embedding problem for planar graphs, showing that four pages are sufficient to book embed a planar graph .
In this paper it is proved that this is not the case (not even for every 5-connected planar graph [G.
However, the number is easily applied to most polyhedra, for by looking 'through a face' of the polyhedron we can obtain a planar graph.
An example of orthogonal embedding of a planar graph is illustrated in Fig.
Observation 2 -- Considering a particular planar graph representation: This observation illustrates how students over emphasize the visual aspect of Graph Theory, and base their answers on a specific planar representation of a graph's vertices and arcs.
For example, the crossing number of a planar graph is 0 and the crossing number of [K.

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