Báo cáo toán học: "The asymptotic number of set partitions with unequal block sizes" pot
Báo cáo toán học: "The asymptotic number of set partitions with unequal block sizes" pot
... the number of partitions of (the number) n,andQis its ordinary
generating function. Also, define p(n, k) to be the number of partitions of n with largest
part at most k. We will have use of the ... values of n, we shall use elementary estimates and some well-known bounds
for ordinary partitions (of a number) to express most values of b
n
in terms of the number...
Báo cáo toán học: "THE INDEPENDENCE NUMBER OF DENSE GRAPHS WITH LARGE ODD GIRTH" ppsx
... 2
−
(
k−1
k
)
n
k−1
k
d
1
k
.
Proof. Immediate from Theorem 3.
This improves Denley’s Theorem 4.
References
1. Denley, T., The Independence number of graphs with large odd girth, The Electronic Journal of
Combinatorics ... d
k
(v)
.
Proof. Randomly label the vertices of G with a permutation of the integers from 1 to
n.LetA (respectively B) be the set of vertices v of G suc...
Báo cáo toán học: "The independence number of graphs with large odd girth" ppt
... vertex of V (G
k−1
)withdegreeatleast
¯
d(G
(k−1)
)then
m
i=1
N
1
i
(v) is an independent set of size
m
i=1
|N
1
i
(v)|≥m
(k−1)
¯
d(G
(k−1)
) .
7
The independence number of
graphs with ... the independence number
of general graphs of a given odd girth. We shall prove some similar bounds to
those we prove for regular graphs in terms of a measure of the concentra...
Báo cáo toán học: "The minimum number of monotone subsequences" pptx
... our sequence of the values in
L
i
and R
i
are disjoint subsets of [s
i
− k +1,s
i
+ k − 2]; let B
i
be the set of positions of
the values in L
i
,andletB
i
be the set of positions of the values ... L = { u : (u) <(v) } be the set of values to
the left of v,andR = { u : (u) >(v) } be the set of values to the right of v.Put
the electronic journal of com...
Báo cáo toán học: "The maximum number of perfect matchings in graphs with a given degree sequence" docx
... permutation of rows and columns A is a
block diagonal matrix in which each block is a square all-1 matrix.
Proof of Theorem 1.1: The square of the number of perfect matchings of G counts
ordered pairs of ... is the number of spanning 2-regular
subgraphs H of G consisting of even cycles (including cycles of length 2 which are the
same edge taken twice), where each s...
Báo cáo toán học: "The crossing number of a projective graph is quadratic in the face–width" doc
... 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 of intersections of G with a noncontractible ... is a subdivision of a diamond grid of size r, which corresponds back
in G to a projective diamond grid minor of size r. ✷
3 Crossing number of projective diam...
Báo cáo toán học: "The Ramsey number of diamond-matchings and loose cycles in hypergraphs" potx
... T
∗
R
is the set of hyperedges of T colored with red by c(x
1
, x
2
). Consider the complete
r −2-uniform hypergraph F ⊂ T
∗
spanned by the vertex set of e ∪f. Among all pairs of
edges of F with distinct ... . . , y
k
of vertices of T so that
at each step y
i
is selected outside the union of the forbidden set for T and the forbidden
set of T
∗
. Then at each step...
Báo cáo toán học: "he spectral gap of random graphs with given expected degrees" pot
... Proofs of Auxiliary Lemmas
7.1 Proof of Lemma 2.2
The proof of Lemma 2.2 relies on the following general tail bound, which is a consequence
of Azuma’s inequality (cf. [17, p. 38] for a proof).
Lemma ... the
volume of the set of vertices removed during the iterative procedure in step K2.
Lemma 3.11 Let T be the set of all vertices removed during the second step K2 of the
co...
