Báo cáo toán học: "New Lower Bound Formulas for Multicolored Ramsey Numbers" pptx
Báo cáo toán học: "New Lower Bound Formulas for Multicolored Ramsey Numbers" pptx
... Classification: 05D10
Abstract
We give two lower bound formulas for multicolored Ramsey numbers. These formu-
las improve the bounds for several small multicolored Ramsey numbers.
1. INTRODUCTION
In ... INTRODUCTION
In this short article we give two new lower bound formulas for edgewise r-colored
Ramsey numbers, R(k
1
,k
2
, ,k
r
), r ≥ 3, defined below. Both formul...
Báo cáo toán học: "New lower bound for multicolor Ramsey numbers for even cycle" doc
... Moreover, by using upper bound for
Ramsey number for even cycles ([5, Section 5.7, Theorem 10]), we have R
3
(C
8
) ≤ 2412,
and by using known upper bound for Ramsey number for symmetric bipartite ... analogously. We refer the reader to [6] for a
survey.
2 The Ramsey numbers for even cycles
Up to now, there have been known only two exact values for 3-color Ramsey num...
Báo cáo toán học: "A Lower Bound for Schur Numbers and Multicolor Ramsey Numbers of K3" doc
... published bounds for
S
(5) are 157 ≤
S
(5) ≤ 321, the lower bound
was proved in [4] and the upper bound in [6]. For Ramsey numbers we know
R
2
(3) = 6 and
R
3
(3) = 17; the current bounds on
R
4
(3) ... 1994; Accepted: September 18, 1994
Abstract
For k ≥ 5, we establish new lower bounds on the Schur numbers S(k)
and on the k-color Ramsey numbers of K
3
.
For integers
m
and...
Báo cáo toán học: " New Lower Bounds for Some Multicolored Ramsey Numbers" pot
... Lower Bounds for Ramsey Numbers
It is amazing that the result of this section has not been observed for the 25 years
since [C] was published. Using this observation we will give 6 new lower bounds.
Currently ... 87-95.
[R] S. Radziszowski, Small Ramsey Numbers, Electronic Journal of Combinatorics,
Dynamic Survey DS1, 1994, 28pp.
[S] Song En Min, New Lower Bound Formulas for...
Báo cáo toán học: "A LOWER BOUND FOR THE NUMBER OF EDGES IN A GRAPH CONTAINING NO TWO CYCLES OF THE SAME LENGTH" pptx
... Zhangzhou Teachers College(Natural Science
Edition) 3(1)(1989) 55-59.
[4] Chunhui Lai, Upper bound and lower bound of f(n), J. Zhangzhou Teachers Col-
lege(Natural Science Edition) 4(1)(1990) 29,30-34.
[5] ... Acknowledgment
The author thanks Prof. Yair Caro and Raphael Yuster for sending reference [7]. The
author also thanks Prof. Cheng Zhao for his advice.
References
[1] J.A. Bond...
Báo cáo toán học: "New lower bounds for Heilbronn numbers" pps
... determination of optimal values and lower
bounds for every H
n
. Besides the trivial cases H
3
and H
4
, Golberg showed constructions
providing lower bounds for n ≤ 15. A.W.M. Dress, Yang Lu, ... value for H
5
.Theyalso
improved the lower bound for H
7
.
In this note, and by using a simple implementation of simulated annealing and a further
optimization procedure, we present n...
Báo cáo toán học: "New upper bound for a class of vertex Folkman numbers" pptx
... − 1) was given in [1]. Here
we shall note only the general bounds for the numbers F (a
1
, ,a
r
; m − 1). In [8] the
following lower bound was proved
F (a
1
, ,a
r
; m − 1) ≥ m + p +2,p≥ 2.
In ... New upper bound for a class of vertex Folkman
numbers
N. Kolev
Department of Algebra
Faculty of Mathematics and Informatics
“St. Kl. Ohridski” University of Sofia
5 ... [4],[6],[7]). For...
Báo cáo toán học: "Sharp lower bound for the total number of matchings of tricyclic graphs" doc
... sharp lower bound for the
Hosoya index of quasi-tree graphs; see [20]. Liu and Lu characterized t he cacti graphs
with minimal Hosoya index in [23]. Machnicka et al. determined sharp bounds for ... with
maximal Hosoya index. For n-vertex bicyclic graphs, Deng [7, 8] determined sharp upper
and lower bounds on Hosoya index of bicyclic graphs, resp ectively.
Recently, for other cla...
Báo cáo toán học: "An Ehrhart Series Formula For Reflexive Polytopes" pptx
... Further, as P is reflexive, all of the lattice points
in R
d
P
are contained in the boundary of kP for some k ∈ N. Therefore, the lattice points
in t(P ⊕ Q) can be partitioned as
k∈{0, ,t}
p
q
: ... that
p
q
∈
∩
i
ˆ
H
i
∩
∩
j
ˆ
K
j
∩ t (P ⊕ Q).
For the “⊇” containment, let
p
q
∈
∩
i
ˆ
H
i
∩
∩
j
ˆ
K
j
∩ t (P ⊕ Q). We know
that p · a
i
≥ 0 for all i, q · b
j...
Báo cáo toán học: " Near optimal bound of orthogonal matching pursuit using restricted isometric constant" docx
... peaking, since K/
√
K −1 ≈
√
K for K ≫ 1, the proposed condition approximates to
δ
K
< 1/(1 +
√
K) for a large K. In order to get an idea how close the prop osed bound is from the limit
conjectured ... proposed bound is expre ssed in terms of δ
K
while (3) and the limit of Dai and
Milenkovic are express ed in terms of δ
K+1
so that the comparison is slightly unfavorable for the p...