Embeddings of cubic Halin graphs: Genus distributions
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.
genus distribution; Halin graph; outerplanar graph; topological graph theory; partial genus distribution.