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Embeddings of Cubic Halin Graphs: Genus Distributions ∗

By Jonathan L. Gross


We derive an O(n2)-time algorithm for calculating the genus distribution of a given 3-regular Halin graph G; that is, we calculate the sequence of numbers g0(G), g1(G), g2(G),... on the respective orientable surfaces S0, S1, S2,.... Key topological features are a quadrangular decomposition of plane Halin graphs and a new recombinant-strands reassembly process that fits pieces together three-at-a-vertex. Key algorithmic features are reassembly along a post-order traversal, with just-in-time dynamic assignment of roots for quadrangular pieces encountered along the tour

Topics: genus distribution, Halin graph, partitioned genus distribution, gram embedding, outerplanar graph, topological graph theory. Math. Subj. Class, 05C10
Year: 2012
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