Báo cáo toán học: "The maximum number of perfect matchings in graphs with a given degree sequence" docx
Báo cáo toán học: "The maximum number of perfect matchings in graphs with a given degree sequence" docx
... square all-1 matrix.
Proof of Theorem 1.1: The square of the number of perfect matchings of G counts
ordered pairs of such matchings. We claim that this is the number of spanning 2-regular
subgraphs ... Cuckler and J. Kahn, Entropy bounds for perfect matchings and Hamiltonian
cycles, to appear.
[3] S. Friedland, An upper bound for the number of perfect matching...
Báo cáo toán học: "The independence number of graphs with large odd girth" ppt
... for graphs of odd girth at least
7. Dealing with graphs with larger odd girth will simply require a generalisation
of this argument.
Theorem 1 Let G be a graph of order n containing containing ... results of this paper are designed to deal with the case when the average
degree of the graph is large. We shall prove that an r-regular graph without 3 and
5 cycles has an...
Báo cáo toán học: "THE INDEPENDENCE NUMBER OF DENSE GRAPHS WITH LARGE ODD GIRTH" ppsx
... ≥
√
n
¯
d2 as claimed.
This improves Denley’s Theorems 1 and 2. It is sharp for the regular complete
bipartite graphs K
aa
.
The above results are readily extended to graphs of larger odd girth.
Lemma ... T., The Independence number of graphs with large odd girth, The Electronic Journal of
Combinatorics 1 (1994) #R9.
2
We can now prove the following theorem.
Theorem 1. Suppose...
Báo cáo toán học: "The asymptotic number of set partitions with unequal block sizes" pot
... Knopfmacher
Department of Computational and Applied Mathematics
University of Witwatersrand
Johannesburg, South Africa
e-mail: arnoldk@gauss.cam.wits.ac.za
A. M. Odlyzko
AT&T Labs - Research
Florham Park, ... estimates and some well-known bounds
for ordinary partitions (of a number) to express most values of b
n
in terms of the number
of ordinary partitions of k with...
Báo cáo toán học: "The minimum number of monotone subsequences" pptx
... permutation. Var-
ious operations were then applied to it: transposing a pair of values in the permutation;
reversing the order of a block of values in the permutation; rotating a block of values ... extremal permutations with 0 and n − 1 adjacent are as described in Theorem 4,
and all such permutations are extremal.
Proof Without loss of generality, suppose a permut...
Báo cáo toán học: "The crossing number of a projective graph is quadratic in the face–width" doc
... Klein, Multiple-source shortest paths in planar graphs. In: SODA 2005, Pro-
ceedings, SIAM (2005), 146–155.
[10] B. Mohar, A linear time algorithm for embedding graphs in an arbitrary surface.
SIAM ... crossing
number of projective graphs with bounded degree.
1 Introduction
We recall that the face–width of a graph G embedded in a surface Σ is the minimum
number...
Báo cáo toán học: "The minimum size of complete caps in (Z/nZ)2" ppt
... paper with a large number of open problems in this area.
1 Introduction
A k-cap in AG(n, q) (a nen-space over F
q
) is a subset X ⊂ AG(n, q)ofsizek,nothree
of whose points are collinear. When a ... q)
10
points. A similar bound holds for the minimum size of a complete cap in
AG(2,q) since we can obtain AG(2,q)fromPG(2,q) by removing a line at in nity.
We can ask...
Báo cáo toán học: "The maximum distinguishing number of a group" ppt
... nilpotent of class c or supersolvable of length c then G acts with
distinguishing number at most c +1.
As a corollary, we obtain that all metacyclic groups act with distinguishing number
at most 3 since ... Collins in [2] as a
property of graphs. More specifically, the distinguishing number of a graph M, denoted
D(M), is the smallest number of colors admitting a...
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