Asymptotic Enumeration of Labelled Graphs by Genus
Copyright policy )Asymptotic Enumeration of Labelled Graphs by Genus
We obtain asymptotic formulas for the number of rooted 2-connected and 3-connected surface maps on an orientable surface of genus $g$ with respect to vertices and edges simultaneously. We also derive the bivariate version of the large face-width result for random 3-connected maps. These results are then used to derive asymptotic formulas for the number of labelled $k$-connected graphs of orientable genus $g$ for $k\le3$.
- University of California, San Diego United States
- Carleton University Canada
Graph labelling (graceful graphs, bandwidth, etc.), asymptotic formula, surface map, labelled graphs, face width, Enumeration in graph theory, orientable genus, Asymptotic enumeration, orientable surface, Planar graphs; geometric and topological aspects of graph theory
Graph labelling (graceful graphs, bandwidth, etc.), asymptotic formula, surface map, labelled graphs, face width, Enumeration in graph theory, orientable genus, Asymptotic enumeration, orientable surface, Planar graphs; geometric and topological aspects of graph theory
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