Báo cáo toán học: "On-line Ramsey Theory for Bounded Degree Graphs" doc
Báo cáo toán học: "On-line Ramsey Theory for Bounded Degree Graphs" doc
... Jiang, K.G. Milans, and D.B. West, Degree Ramsey number of cycles is bounded,
submitted.
[16] H.A. Kierstead and G. Konjevod, Coloring number and on-line Ramsey theory for
graphs and hypergraphs Combin ... on-line degree Ramsey numbers for trees and cycles,
draft.
[18] W.B. Kinnersley, K.G. Milans, and D.B. West, Degree Ramsey numbers of graphs,
submitted.
[19] J. Neˇset...
Báo cáo toán hoc:" Anti-Ramsey numbers for graphs with independent cycles Zemin Jin" ppt
... of anti -Ramsey numbers for Ω
k
Unlike graphs in the family Ω
2
, we have no more information about graphs in the family
Ω
k
for k ≥ 3. So we cannot treat the family Ω
k
(k ≥ 3) as we did for the ... anti -Ramsey numbers o f cycles,
J. Graph Theory 47 (2004), 9-28.
[4] B. Bollob´as, Extremal Graph Theory, Academic Press, New York, 1978.
[5] P. Erd˝os, M. Simonovits, and V.T. S´os,...
Báo cáo toán học: "Short generating functions for some semigroup algebras" doc
... binomials of the form x
α
i
−
j=i
x
β
j
j
.Nowuse
induction on the degree of such binomials.
Let J = p
1
,p
2
,p
3
.IfJ = I, then choose b = x
α
i
−
j=i
x
β
j
j
of smallest degree in I\J.
By ... s
12
and
s
13
are nonzero: then either b
= x
i
b
for some binomial b
and i = 2 or 3. The degree of
b
is less than that of b,sob
∈ J; therefore b
would be too.
Conseque...
Báo cáo toán học: "MacMahon-type Identities for Signed Even Permutations" docx
... L
n
. Therefore by induction π = π
0
π
n−2
π
n−1
with π
j
∈ R
L
j
for all 0 ≤ j ≤ n − 1.
For example, let π =[3, 5, −4, 2, −1], then π
3
= a
3
a
2
a
1
; ππ
−1
3
=[−4, 3, 2, −1, 5], there-
fore π
2
= ... 3.1 and 3.3]. For a proof
of the general case, see for example [2, Ch. 3.3].
the electronic journal of combinatorics 11 (2004), #R83 3
From this formulation one sees immediately that...
Báo cáo toán học: "Constructive Upper Bounds for Cycle-Saturated Graphs of Minimum Size" doc
... vertex. However, in constructing W (n, 2k +2) we have
forbidden this to occur for spokes this close. Thus no cycle of length l exists.
Lemma 2 For any edge e in the complement of W (n, 2k +2) and ... value of this function for a given graph F has been quite difficult, and is known for
relatively few graphs. K´aszonyi and Tuza in [12] proved the best known general upper
bound for sat(n...
Báo cáo toán học: "Sharp threshold functions for random intersection graphs via a coupling method" potx
... property “minimum degree at least k” is
increasing, the result for larger ω follows by a simple coupling argument applied to
G (n, m, ·). The vertex degree analysis becomes complex for α near 1 due ... the degree distribution [18]
and the phase transition [13] for α = 1. Although they consider p near phase transition
threshold, they show that, for some properties, there is a val...
Báo cáo toán học: "Ramanujan Type Congruences for a Partition Function" docx
... Int. J. Number Theory, 6 (2010), 673–680.
[6] H C. Chan, Ramanujan’s cubic continued fraction and Ramanujan type congruences
for a ceratin par titio n function, Int. J. Number Theory, 6 (2010), ... was also proven by Baruah and Ojah [1] using the 3-dissections for ϕ(−q)
−1
and ψ(q)
−1
, and by Cao [4] applying the 3-dissection for (q; q)
∞
(q
2
; q
2
)
∞
. We will give
another proof b...