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Enumeration of boundary cubic inner-forest maps. (English) Zbl 1289.05258
Summary: This paper investigates the number of boundary cubic inner-forest maps and presents some formulae for such maps with the size (number of edges) and the valency of the root-face as two parameters. Further, by duality, some corresponding results for rooted outer-planar maps are obtained. It is also an answer to the open problem in [W. Liu et al., Discrete Appl. Math. 155, No. 13, 1678–1688 (2007; Zbl 1122.05029)] and corrects the result on boundary cubic inner-tree maps in that article.
MSC:
05C45 Eulerian and Hamiltonian graphs
05C30 Enumeration in graph theory
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