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Neighbor-Net produces circular collections of splits depicted by a planar graph with boxes.
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In an equivalent graph-theoretic form, one may translate this problem to ask whether the vertices of a planar graph can always be coloured by using just four colours in such a way that vertices joined by an edge have different colours.
Therefore by Theorem 1, ({mathbb {G}}({mathbb {Z}}_n)) is a planar graph.
Now, by Theorem 1, we find that ({mathbb {G}}({mathbb {Z}}_n)) is a planar graph.
A planar graph is one in which the edges have no intersection or common points except at the edges.
Paul Chew, There is a Planar Graph Almost as Good as the Complete Graph, Symposium on Computational Geometry (1986), 169-177.
K5 is not a planar graph, because there does not exist any way to connect every vertex to every other vertex with edges in the plane such that no edges intersect.
If G is a planar graph of diameter 2.
A plane graph is a planar graph together with an embedding in the plane.
A planar graph is called a maximal planar graph if for every pair of nonadjacent vertices u and v of G, the graph G + u v is nonplanar.
A distributed algorithm is first implemented to obtain a planar graph.
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