combinatorial decompositions
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2021 ◽  
Vol 104 ◽  
pp. 630-652
Author(s):  
Michela Ceria




2012 ◽  
Vol 33 (5) ◽  
pp. 688-711 ◽  
Author(s):  
Binh-Minh Bui-Xuan ◽  
Michel Habib ◽  
Michaël Rao




10.37236/1787 ◽  
2004 ◽  
Vol 11 (1) ◽  
Author(s):  
Philippe Flajolet ◽  
Bruno Salvy ◽  
Gilles Schaeffer

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 enumeration results using only first principles of combinatorial analysis and straight asymptotic analysis—specifically, the saddle-point method. In this perspective, the enumeration of connected graphs by excess (of number of edges over number of vertices) derives from a simple saddle-point analysis. Furthermore, a refined analysis based on coalescent saddle points yields complete asymptotic expansions for the number of graphs of fixed excess, through an explicit connection with Airy functions.



2000 ◽  
Vol 217 (1-3) ◽  
pp. 101-113 ◽  
Author(s):  
Manoj K. Chari


COMBINATORICA ◽  
1991 ◽  
Vol 11 (3) ◽  
pp. 275-293 ◽  
Author(s):  
Bernd Sturmfels ◽  
Neil White


1987 ◽  
Vol 9 (1-2) ◽  
pp. 71-81 ◽  
Author(s):  
V. K. Oganian


1983 ◽  
Vol 83 (1) ◽  
pp. 6-19
Author(s):  
Kenneth Baclawski


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