Báo cáo toán học: "Entrywise Bounds for Eigenvectors of Random Graphs" docx
Báo cáo toán học: "Entrywise Bounds for Eigenvectors of Random Graphs" docx
... entrywise bounds for second and lower eigenvectors of
adjacency matrix of Planted partition models. We make a step towards resolving these
questions through computing entrywise bounds for the second ... entrywise
perturbation for eigenvectors of Random graphs, i.e. v
1
(A) −v
1
(E(A))
∞
(where v
1
(M)
is the first eigenvector of a square symmetric matrix M). Perturbat...
Báo cáo khoa học:Tight estimates for eigenvalues of regular graphs docx
... is
at most 1 for i =2andd = 4, and at most 1 for i =3andd = 3. It follows that for all
d ≥ 3, i
0
+1≤ 3, whereas for d ≥ 5, i
0
+1=1.
Put x
i
= y
i+i
0
for all i,0≤ i ≤ 2k − i
0
. Therefore, x
i
is ... is a decreasing function of i for all admissible values of i, and hence we simply
let i
0
+ 1 be the smallest i for which this ratio is at most 1. (Such an i exists, as for...
Báo cáo toán học: "Balanced online Ramsey games in random graphs" docx
... monochromatic copy of some fixed
graph F for as long as possible.
We prove explicit threshold functions for the duration of this game for an arbi-
trary number of colors r and a large class of graphs F ... Given a random graph with rN edges and a random partition of
these edges into sets of size r, is there an r-edge-coloring avoiding monochromatic copies
of F such that...
Báo cáo toán học: " Sharp bounds for Seiffert mean in terms of root mean square" pot
... below).
For information about publishing your research in Journal of Inequalities and Applications go to
http://www.journalofinequalitiesandapplications.com/authors/instructions/
For information ... 64p
3
+ 36p
2
− 12p + 1, (2.10)
6
holds for all a, b > 0 with a = b if and only if α ≤ (1 +
16/π
2
− 1)/2 and
β ≥ (3 +
√
6)/6.
2 Proof of Theorem 1.1
Proof of Theorem 1.1. Let λ...
Báo cáo toán học: "The Bounds on Components of the Solution for Consistent Linear Systems" pdf
... immediately from Theorem 3.1
of [3].
Vietnam Journal of Mathematics 33:1 (2005) 91–95
The Bounds on Components of the Solution
for Consistent Linear Systems
*
Wen Li
Department of Mathematics, South ... 1–8.
4. W. Li, On the property of solutions of
M-matrix equations, Systems Science and
Math. S cience 10 (1997) 129–132.
The Bounds on Comp onents of the Solution for Con...
Báo cáo toán học: "New Bounds for Codes Identifying Vertices in Graphs" pdf
... Lower bounds
For a given finite regular graph G =(V,E), let B = |B(v)| denote the size (indepen-
dent of its centre) of a ball of radius one; let C be an identifying code. Since C is a
covering of ... D(C)ofC ⊆ V is
defined as |C|/|V | for
nm
and for the infinite graph as
D(C) = lim sup
n→∞
|C ∩Q
n
|
|Q
n
|
where Q
n
is the set of vertices (x, y) ∈ V such that |x|≤n and |y|...
Báo cáo toán học: " New Bounds for Union-free Families of Sets" potx
... elements of A.
Consider the partition, P , of the elements of F into groups depending on
the value of A ∪ B,B ∈ F. By the choice of A at least
1
2n
2
αn
elements of
F lie in groups of size at ... yield bounds on the size of union-free families.
the electronic journal of combinatorics 5 (1998), # R39 11
4 Lower bound on f
We give a construction of a (strongly) union-free...
Báo cáo toán học: "Asymptotic Bounds for Bipartite Ramsey Numbers" pot
... coloring of the edges of
K
r,r
contains either a red K
m,m
or a green
K
n,n
. We obtain asymptotic bounds for
b
(m, n
) for
m ≥
2 fixed and n → ∞.
1 Introduction
Recent exact results for bipartite ... [6]. Consider a random coloring of the edges of K
r,r
in which, independently,
each edge is colored red with probability p
. For each set S of 2
m vertices, m from each
vert...
Báo cáo toán học: "General bounds for identifying codes in some infinite regular graphs" docx
... ≤
8r − 8
9r
2
− 16r
for r ≡ 0mod4,
8
9r − 25
for r ≡ 1mod4,
8
9r − 34
for r ≡ 2mod4,
8r − 16
(r − 3)(9r − 43)
for r ≡ 3mod4.
For the square lattice:
the electronic journal of combinatorics 8 (2001), ... values of r. The square lattice with two diagonals is considered in [4] and [3].
2 General lower bounds
We conside...
Báo cáo toán học: "Improved bounds for the number of forests and acyclic orientations in the square lattice" doc
... L
n
. There the authors gave the following bounds for the asymp-
totics of f(n), the number of forests of L
n
,andα(n), the number of acyclic orienta-
tions of L
n
:3.209912 ≤ lim
n→∞
f(n)
1/n
2
≤ ... =(V,E), a forest of G is a subset A of E that contains no cycle.
A spanning forest of G is a spanning subgraph whose edge set is a forest. An acyclic
orientation of G is an...
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