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

... Asymptotic enumeration of labelled graphs by genus Edward A. Bender Department of Mathematics University of California at San Diego La Jolla, CA 92093-0112, USA ebender@ucsd.edu Zhicheng Gao ∗ School of ... number of labelled k-connected graphs of orientable genus g for k ≤ 3. 1 Introducti on The exact enumeration of various types of maps on the sphere (or, equiv...

Ngày tải lên: 08/08/2014, 12:23

... small values of m and n, we can extract the constant term of G by using a method of summing over roots of unity. A technique of this nature was given by Good and Crook [9] and improved by McKay [12]. ... by degree sequence of graphs of high degree. European J. Combinatorics, 11 (1990) 565–580. [16] B. D. McKay and N. C. Wormald, Asymptotic enumeration by degree seq...

Ngày tải lên: 07/08/2014, 13:21

... express the (−1) enumeration of self–complementary plane partitions in terms of SC(a, b, c), the ordinary enumeration of self–complementary plane partitions. Theorem 2. The enumeration of self–complementary ... remaining cases of the weighted enumeration of self–complementary plane partitions contained in a given box where adding one half of an orbit of cubes and removi...

Ngày tải lên: 07/08/2014, 08:22

... the problem of enumeration of planar near-triangulations, solved by Tutte in [9] using the method of recursive decomposition. The same method, applied to the problem of enumeration of triangulations ... planar map is a class of equivalence of embedded graphs G → S 2 by the homeomor- phisms of S 2 . We note by V (G), E(G) and F (G) the sets of vertices, edges and...

Ngày tải lên: 07/08/2014, 15:23

... argument to complete the proof. The proof of equation (18) is similar to that of (14) using the idea of the proof of (17). We omit the details. Remark. The idea of using the sets M and M + (multiple ... by starting with the set M used in the proof of (9) , with k replaced by k + m. This set M has cardinality C p−k−m,(k+m)t+r . With k + m segments, we select m of them the ele...

Ngày tải lên: 08/08/2014, 12:23

... factorisations, see Chapter 11 of [14]. One of the ideas there is that of a train, which we now define for factorisations of complete bipartite graphs. Suppose we have G,acopyofK n,n in which the vertex ... only one infinite family of perfect 1-factorisations of complete graphs known. For prime p theideaistoconsiderK 2p as the union of two graphs: K p,p and a double copy of...

Ngày tải lên: 07/08/2014, 06:20

... Subclaims, the proof of our lemma is complete. 5 Proof of the Main Theorem In this section, we present the proof of the main theorem. Let C be a topologically closed class of graphs with den(G) ... digit of y is 3 and z is not a member of the second coordinate of the label of y, delete the edge x j y.If the digit of z is 3 and y is not a member of the second coordinate...

Ngày tải lên: 07/08/2014, 06:23

... The set of partial latin squares of order n is denoted by PLS(n), and the set of latin squares of order n by LS(n). We say that P 1 ∈ PLS(n) contains P 2 ∈ PLS(n) if every filled cell of P 2 agrees ... A is a copy of M, B = C is a copy of J with each symbol increased by m and D is a copy of M in which each of the cells in M \ J has had its symbol increased by m. Notic...

Ngày tải lên: 07/08/2014, 06:23

... ordering of the vertices to an ordering of the edges lexicographically. A broken circuit of H ⊆ G is a set of edges B ⊆ H such that there is some edge e ∈ G, smaller than every edge of B, such ... consists of all edges of G with both ends in S. We will use the symbols π and σ to denote set partitions. The notation π  S means π is a set partition of the set S. The length (numb...

Ngày tải lên: 07/08/2014, 08:22

... one-factorization of type 4 + 4 + 4 is only possible for three graphs of order 12: the disjoint union of three copies of C 4 , the disjoint union of three copies of K 4 ,and the union of K 4 and the ... for classifying one-factorizations of regular graphs are studied. The smallest open case is currently graphs of order 12; one-factorizations of r-regular graphs of...

Ngày tải lên: 07/08/2014, 08:22