TAILIEUCHUNG - Báo cáo toán học: "Asymptotic enumeration of labelled graphs by genus"

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Department of Mathematic dành cho các bạn yêu thích môn toán học đề tài: Asymptotic enumeration of labelled graphs by genus. | Asymptotic enumeration of labelled graphs by genus Edward A. Bender Zhicheng Gao Department of Mathematics School of Mathematics and Statistics University of California at San Diego Carleton University La Jolla CA 92093-0112 USA Ottawa Canada K1S 5B6 ebender@ zgao@ Submitted Mar 14 2010 Accepted Dec 17 2010 Published Jan 12 2011 Mathematics Subject Classification 05A16 05C30 Abstract 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 facewidth 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 3. 1 Introduction The exact enumeration of various types of maps on the sphere or equivalently the plane was carried out by Tutte 26 27 28 in the 1960s via his device of rooting. Terms in this paragraph are defined below. Building on this explicit results were obtained for some maps on low genus surfaces . as done by Arques on the torus 1 . Beginning in the 1980s Tutte s approach was used for the asymptotic enumeration of maps on general surfaces 3 12 4 . A matrix integral approach was initiated by zt Hooft see 21 . The enumerative study of graphs embeddable in surfaces began much more recently. Asymptotic results on the sphere were obtained in 8 22 20 and cruder asymptotics for general surfaces in 22 . In this paper we will derive asymptotic formulas for the number of labelled graphs on an orientable surface of genus g for the following families 3-connected and 2-connected with respect to vertices and edges and 1-connected and all with respect to vertices. Along the way we also derive results for 2-connected and 3-connected maps with respect to vertices and edges. The result for all graphs as well as various parameters for these graphs was announced .

Đã phát hiện trình chặn quảng cáo AdBlock
Trang web này phụ thuộc vào doanh thu từ số lần hiển thị quảng cáo để tồn tại. Vui lòng tắt trình chặn quảng cáo của bạn hoặc tạm dừng tính năng chặn quảng cáo cho trang web này.