Airy Phenomena and the Number of Sparsely Connected Graphs
نویسندگان
چکیده
The enumeration of connected graphs by excess (number of edges minus number of vertices) is a well-understood problem usually dealt by means of combinatorial decompositions or indirect formal series manipulations. In their work [3], Philippe Flajolet, Bruno Salvy, and Gilles Schaeffer derive such enumerative results mainly using analytic methods. In particular, they exhibit strong connections between Airy functions and the complete asymptotic expansions of the number of connected graphs of fixed excesses.
منابع مشابه
Airy Phenomena and Analytic Combinatorics of Connected Graphs
Until now, the enumeration of connected graphs has been dealt with by probabilistic methods, by special combinatorial decompositions or by somewhat indirect formal series manipulations. We show here that it is possible to make analytic sense of the divergent series that expresses the generating function of connected graphs. As a consequence, it becomes possible to derive analytically known enum...
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