Báo cáo toán học: "New Upper Bounds for the Size of Permutation Codes via Linear Programmin" pdf
Báo cáo toán học: "New Upper Bounds for the Size of Permutation Codes via Linear Programmin" pdf
... new bounds for µ(n, d) for small values of the param-
eters n and d. In [15], H. Tarnanen uses the conjugacy scheme of the group S
n
in order
to obtain new upper bounds fo r the size of a permutation ... obtain sharper
upper bounds, other linear constraints on the coefficents a
i
must be considered. The
following theorem motivates the study of permutati...
Báo cáo toán học: "NEW UPPER BOUNDS ON THE ORDER OF CAGES1" pps
... provide upper bounds on the orders of (k, g)-cages.
Namely,
Theorem 2.1 [7] Let G be a k-regular graph of girth at least g having the least
number of vertices. Then the girth of G is g and the diameter ... by F¨uredi, Seress and the authors,
see [9]. The fact that the orders of these constructions actually meet the upper
bound in (2) for q odd follows from [1...
Báo cáo toán học: "TIGHT UPPER BOUNDS FOR THE DOMINATION NUMBERS OF GRAPHS WITH GIVEN ORDER AND MINIMUM DEGREE" pdf
... contains the value of γ(n, δ) for n ≤ 16, 0 ≤ δ ≤ n − 1 if the value is
known, otherwise upper and lower bounds for γ(n, δ). We establish these values in
Sections 2, 3 and 4.
TIGHT UPPER BOUNDS FOR THE ... either two A
v
’s of
the form {x, z} and {y,w} or, of the form {x, w} and {y, z}. But this contradicts
our assumption that the two element A
v
’s are never d...
Báo cáo toán học: "Tight Upper Bounds for the Domination Numbers of Graphs with Given Order and Minimum Degree, II." pdf
... definition of δ
k
(n). The theorem
therefore follows.
In the next section we show that if k = 3 then the above theorem holds for n ≥ 6.
Note that the results in this section are stated for fixed ... The theorem therefore follows from the
definition of δ
k+1
(n) which is the maximum value of δ for which γ(n, δ) ≥ k +1.
We shall show that this upper bound is quite tight...
Báo cáo toán học: "New upper bound for a class of vertex Folkman numbers" pptx
... automorphism of Γ
p
. (4)
The graph Γ
p
was defined for the first time in [8]. In [8] it is also proved that Γ
p
→ (3,p)
for p ≥ 3. For the proof of the main theorem we shall also use the following ... have
cl(G
i
)=a
i
− 1 for i =1, 2. (14)
From (13), (14) and Lemma 1 we conclude that
The number of the vertices of each connected
component of
¯
G
1
is an even num...
Báo cáo toán học: "Improved Upper Bounds for the Laplacian Spectral Radius of a Graph" docx
... (14) is the best in all known upper
bounds for G
2
, and bound (18) is the best in all known upper bounds for G
3
. Finally,
bound (22) is the best upper bound for G
1
and bound (1 8) is the second-best ... r
i
=
j=i
|a
ij
| for each i = 1, 2 , . . . , n, then
Lemma 2.2.
[15]
Let A = (a
ij
) be a complex matrix of order n 2. Then the eigenvalues
of the m...
Báo cáo toán học: " New Lower Bounds for Some Multicolored Ramsey Numbers" pot
... K
k
J
in the upper left submatrix of T
r+3
(of size 3(M − 1) × 3(M − 1)),
then there must be a J-colored K
k
J
in T
r+2
(0, 2, 3, 4, ,r + 3), contradicting the
definition of T
r+2
.
Remark: Up to the ... exactly the same places as in the upper
left block, A. We further note that if (s, t)and(u, v) are two of the entries in question,
then (s, t) ≡ (u, v)(mod M −1) (co...
Báo cáo toán học: "Improved Upper Bounds for Self-Avoiding Walks in Zd" ppt
... approximations of the roots for
specific values of d are found easily, and so are the inverses of the roots of
smallest modulus giving us the entries of first line of table 2.
the electronic journal of combinatorics ... eight.
However, the determination of the asymptotic behavior of the number of
walks of finite memory is much easier.
We can use the auto...
Báo cáo toán học: "New lower bounds for Heilbronn numbers" pps
... stationary
points of f, see [5] for more details. The fulfilment of this condition together with the
context of the situation serves to characterise the local maxima of f.
As an illustration of the local ... with area log n/n
2
for every fixed n; lower bounds on higher
dimensional versions of the problem, produced in 1999 by G. Barequet [2] and the study
of th...
Báo cáo toán học: "Constructive Upper Bounds for Cycle-Saturated Graphs of Minimum Size" doc
... spoke. As the set of spokes form an edge-cut of the graph W (n, 2k +3), such
a cycle must in fact use an even number of spokes. If the number of spokes used is four
or more then the number of vertices ... number of vertices from the hub.
the electronic journal of combinatorics 13 (2006), #R29 4
Constructive Upper Bounds for
Cycle-Saturated Graphs of Minimum...