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Counting unicursal planar near-triangulation. (English) Zbl 1358.05170
Summary: A map is unicursal if all its vertices are even-valent except two odd-valent vertices. A near-triangulation is a map with all but one of its face triangles. This paper investigates the enumeration of rooted unicursal planar near-triangulation and provides two functional equations satisfied by its generating functions with the root-face valency, the number of edges and the number of nonrooted vertices of maps as parameters.
05C45 Eulerian and Hamiltonian graphs
05C30 Enumeration in graph theory
05A15 Exact enumeration problems, generating functions
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