On convex greedy embedding conjecture for 3-connected planar graphs
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
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A well-known Tutte's theorem claims that every 3-connected planar graph has a convex embedding into the plane. Tutte's arguments also show that, moreover, for every nonseparating cycle C of a 3-connected graph G, there exists a convex embedding of G such that C is a boundary of the outer face in this embedding. We give a simple proof of this last result. Our proof is based on the fact that a 3-connected graph admits an ear assembly having some special properties with respect to the nonseparating cycles of the graph. This fact may be interesting and useful in itself. © 2000 John Wiley & Sons, Inc. J. Graph Theory 33: 120–124, 2000