| 31. | This is hard to search for since you just get results for " planar graph ".
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| 32. | For a planar graph, the nullity is equal to the number of meshes in the graph.
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| 33. | They generalize to matroids the notions of planar graph duality and of dual spaces in linear algebra.
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| 34. | However, W . T . Tutte showed that all 4-connected planar graphs are hamiltonian.
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| 35. | Apollonian networks are the maximal planar graphs formed by repeatedly splitting triangular faces into triples of smaller triangles.
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| 36. | F�ry's theorem states that any planar graph may be represented as a planar straight line graph.
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| 37. | However, unlike treewidth, the branchwidth of planar graphs may be computed exactly, in polynomial time.
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| 38. | This in contrast to treewidth for which the complexity on planar graphs is a well known open problem.
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| 39. | In particular, there exists a planar graph without 4-cycles that cannot be 3-colored.
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| 40. | Every maximal planar graph with five or more vertices has vertex connectivity 3, 4, or 5.
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