Efficient enumeration of sensed planar maps
نویسندگان
چکیده
منابع مشابه
Enumeration of planar 2 - face maps 1
Up to now, most of the work on maps has dealt with rooted maps, that is, maps with a distinguished and directed edge. We get rid of this restriction in the case of planar maps having two faces. We enumerate these maps according to their vertex and face degree distributions. The following classes of non rooted 2-face maps are treated: (vertex) labelled or unlabelled, embedded in the plane or on ...
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We enumerate unrooted planar maps (up to orientation preserving homeomorphism) having two faces, according to the number of vertices and to their vertex and face degree distributions, both in the (vertex) labelled and unlabelled cases. We rst consider plane maps, i.e., maps which are embedded in the plane, and then deduce the case of planar (or sphere) maps, embedded on the sphere. A crucial st...
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Sum-free enumerative formulae are derived for several classes of rooted planar maps with no vertices of odd valency (eulerian maps) and with two vertices of odd valency (unicursal maps). As corollaries we obtain simple formulae for the numbers of unrooted eulerian and unicursal planar maps. Also, we obtain a sum-free formula for the number of rooted bi-eulerian (eulerian and bipartite) maps and...
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A planar map is an embedding of a connected planar graph in the sphere such that the surface is partitioned into simply connected regions; in other words, it is a finite cellular decomposition of the sphere into vertices, edges, and faces (0−, 1− and 2−cells, respectively). In particular, 3−connected planar maps correspond to polyhedra. Motivated by the Four Colour Problem, W. Tutte [4] launche...
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We derive closed formulae for the numbers of rooted maps with a fixed number of vertices of the same odd degree except for the root vertex and one other exceptional vertex of degree 1. The same applies to the generating functions for these numbers. Similar results, but without the vertex of degree 1, were obtained by the first author and Rahman. We also show, by manipulating a recursion of Bout...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2005
ISSN: 0012-365X
DOI: 10.1016/j.disc.2004.08.036