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Enumeration of Rooted Cubic Planar Maps
Zhicheng Gao1, and Nicholas C. Wormald2
1Department of Mathematics and Statistics, Carleton University, Ottawa, Canada K1S 5B6
zgao@math.carleton.ca
2Department of Mathematics and Statistics, University of Melbourne, Parkville, VIC 3052 Australia
nick@ms.unimelb.edu.au
Annals of Combinatorics 6 (3) p.313-325 September, 2002
AMS Subject Classification: 05C30
Abstract:
Although much work has been done on enumerating rooted planar maps since Tutte's pioneering works in early 1960s, many classes of maps with no loops or multiple edges are still untreated. In this paper, we enumerate three classes of cubic planar maps with no loops or multiple edges: 1-connected; 2-connected; 3-connected and triangle-free.
Keywords: planar map, cubic planar map, generating function, asymptotic enumeration

References:

1. E.A. Bender, Asymptotic methods in enumeration, SIAM Rev. 16 (1974) 485ĘC515.

2. G. Brinkmann and B.D. McKay, Fast generation of non-isomorphic planar cubic graphs, preprint.

3. W.T. Tutte, A census of planar triangulations, Canad. J. Math. 14 (1962) 21ĘC38.

4. W.T. Tutte, The enumerative theory of planar maps, In: A Survey of Combinatorial Theory, J.N. Srivastava et al. Eds., North-Holland, Amsterdam, 1973, pp. 437ĘC448.