Abstract
In this paper, we introduce three operations on planar graphs that we call face splitting, double face splitting, and subdivision of hexagons. We show that the duals of the planar 4-connected graphs can be generated from the graph of the cube by these three operations. That is, given any graphG that is the dual of a planar 4-connected graph, there is a sequence of duals of planar 4-connected graphsG 0,G 1, …,G n such thatG 0 is the graph of the cube,G n=G, and each graph is obtained from its predecessor by one of our three operations.
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Research supported by a Sloan Foundation fellowship and by NSF Grant#GP-27963.
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Barnette, D. Generating planar 4-connected graphs. Israel J. Math. 14, 1–13 (1973). https://doi.org/10.1007/BF02761529
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DOI: https://doi.org/10.1007/BF02761529