Báo cáo toán học: "Degree distributions in general random intersection graphs" pptx
Báo cáo toán học: "Degree distributions in general random intersection graphs" pptx
... del are recently investigated;
for example, independent sets [11] and component evolution [1, 10]. A generalized random
intersection graph is introduced in [5] by allowing a more general connection ... Component evolution in random intersection gr aphs. The Electronic
Journal of Combinatorics, 14, #R17 , 2007.
[2] M. Bloznelis, Degree distribution of a typical vertex in a gen...
Báo cáo toán học: "Sharp threshold functions for random intersection graphs via a coupling method" potx
... many
properties in random intersection graphs. This method is used to establish sharp
threshold functions in random intersection graphs for k–connectivity, perfect match-
ing containment and Hamilton ... Hamilton cycle containment.
1 Introduction
In a general random intersection graph G(n, m, P
(m)
), as defined in [9], each vertex v
from a vertex set V (| V| = n) is assi...
Báo cáo toán học: "Degree powers in graphs with forbidden subgraphs" docx
... ,
proving (8).
Inequality (9) follows easily, since, in fact, for every p>3, the function g (x)hasa
local minimum at 0. ✷
5 H-free graphs
In this section we are going to prove the following ... (5), we obtain that
(r −1)
n
p +1
+
2n
p +1
<n.
Letting n →∞, we see that p ≥ r, contradicting the assumption and completing the
proof. ✷
Maximizing independently each summand in (3...
Báo cáo toán hoc:"Degree powers in graphs with a forbidden even cycle" pdf
... e
G
(X) for the number of edges induced by X;
- e
G
(X, Y ) for the number of edges joining vertices in X to vertices in Y ;
- G −u for the graph obtained by removing the vertex u ∈ V (G) ;
- Γ
G
(u) ... graph G − u into the sets
A = Γ
G
(u) and B = V (G) \(Γ
G
(u) ∪ {u}) . Since G contains no C
2k+ 2
, the graph G −u
does not contain a path of order 2k + 1 with both ends in A. Applying...
Báo cáo toán học: "Exact Mixing in an Unknown Markov Chain" pptx
... distribution. Using this approach Aldous [3] comes within total variation of the
stationary distribution in time polynomial in 1/ and linear in the maximum hitting time of
the chain.
Since it is ... (randomized) algorithm for exact mixing in an unknown chain has now been
devised by J.G. Propp and D.B. Wilson, using the elegant notion of “coupling from the past.”
Their stopping rule...
Báo cáo toán học: " On the chromatic number of intersection graphs of convex sets in the plane" ppt
... two
points in F
m
are ‘far’ (i.e., on distance more than 2) and the corresponding points in
S
m
do not coincide, then these corresponding points also are ‘far’ apart, and that if two
points in F
m
are ... the claims.
Let L be a supporting line for A at (−z,0), i.e. a line passing through (−z, 0) and
having no common points with the interior of A. Such a line exists, since A is convex.
I...
Báo cáo toán học: "On domination in 2-connected cubic graphs" pps
... graph G containing F
i
and any dominating set D in G, the set
D has at least 9 vertices in V (F
i
).
If D contains neither x
i
nor y
i
, then by Claim 1 D must contain 3 vertices in each of
V ... bound was proved in [2] by exploiting Reed’s techniques
in [9] and examining some of the cases in Reed’s proof more carefully and adding a dis-
charging argument. However, exploting Reed’...
Báo cáo toán học: "Large holes in quasi-random graphs" pptx
... checking if the given graph is (d; ε
1
, ε
2
)-regular we need to consider only sets of the
size ε
1
|V
i
|, i = 1, 2.
In the following section we state our main results proved in Sections 3. In ... bipartite subgraph that can be contained in a (d; ε)-regular graph.
3 The Proof of Theorem 2.1
Before we prove Theorem 2.1, we state a result showing how, by using random graphs,
one can...
Báo cáo toán học: "Consistent cycles in 1 -arc-transitive graphs 2" ppsx
... going between the rings induce the
other three consistent cycles in the orbit.
Now consider the drawing of the Doyle-Holt graph in Figure 2. Here the vertices
are arranged in four concentric rings, ... of cyclets contained in A. In particular, A is a union of distinct G-orbits of
1
k
-consistent cyclets (each being a “shift” of a fixed one).
We can now state and prove the main resu...
Báo cáo toán hoc:" Rainbow matchings in r-partite r-graphs" pps
... sharing
an edge, h as an s-colored t-matching contained in its union.
In the case r = 2 the conjecture is that a set of t+1 disjoint t-matchings has a t-rainbow
matching. This is yet another generalization ... similar, with one main difference: instead of
leaving each matching M
i
after o ne edge, we continue choosing edges from it, until all
edges in some matching M
j
represented in K...
Từ khóa: