Báo cáo toán học: "Asymptotic enumeration of labelled graphs by genus" docx
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...
Báo cáo toán học: "Asymptotic Enumeration of Dense 0-1 Matrices with Equal Row Sums and Equal Column Sums" docx
... 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...
Báo cáo toán học: "(−1)–enumeration of self–complementary plane partitions" ppsx
... 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...
Báo cáo toán học: "Explicit enumeration of triangulations with multiple boundaries" pps
... 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...
Báo cáo toán học: "The Enumeration of Sequences with Restrictions on their Partial Sum" docx
... 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...
Báo cáo toán học: "Perfect factorisations of bipartite graphs and Latin squares without proper subrectangles" pptx
... 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...
Báo cáo toán học: "Competitive Colorings of Oriented Graphs" docx
... 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...
Báo cáo toán học: "A Generalisation of Transversals for Latin Squares'''' docx
... 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...
Báo cáo toán học: "A partition of connected graphs Gus Wiseman" pps
... 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...
Báo cáo toán học: "One-Factorizations of Regular Graphs of Order 12" pot
... 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...