| 41. | Strangulated graphs are graphs that can be formed by clique-sums of chordal graphs and maximal planar graphs.
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| 42. | Flat embeddings are automatically linkless, but not vice versa . and include the planar graphs and apex graphs.
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| 43. | If a planar graph is embedded on a sphere, its face cycles clearly satisfy Lefschetz's property.
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| 44. | The Circle packing theorem states that the intersection graphs of non-crossing circles are exactly the planar graphs.
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| 45. | Frederickson proposed another faster algorithm for single source shortest paths by implementing separator theorem in planar graphs in 1986.
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| 46. | Therefore, by Steinitz's theorem, it is a 3-vertex-connected simple planar graph.
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| 47. | In planar graphs, the set of bounded cycles of an embedding of the graph forms a cycle basis.
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| 48. | The minimum weight cycle basis of a planar graph corresponds to the Gomory Hu tree of the dual graph.
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| 49. | The method of for combining circle packings and quadtrees to achieve bounded slope number for planar graphs with bounded degree
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| 50. | However, a three-dimensional analogue of the planar graphs is provided by the topologically linked with each other.
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