Báo cáo toán học: "On some Ramsey numbers for quadrilaterals" pot
Báo cáo toán học: "On some Ramsey numbers for quadrilaterals" pot
... On some Ramsey numbers for quadrilaterals
Janusz Dybizba´nski Tomasz Dzido
Institute of Informatics
University of Gda´nsk, Poland
jdybiz@inf.ug.edu.pl, ... computer
methods we improve lower and upper bounds for some other multicolor Ramsey
numbers involving q uadrilateral C
4
. We consider 3 and 4-color numbers, our results
improve known bounds.
1 Introduction
In ... Small R...
Báo cáo toán học: "On some Ramsey and Tur´n-type numbers for paths a and cycles" doc
... J., Klamroth K., Mengersen I.: Three color Ramsey numbers for small graphs,
Util. Math. 49 (1996) 85–96.
[2] Bondy J.A., Erd˝os P.: Ramsey numbers for cycles in graphs, J. Combin. Theory Ser.
B ... experience from calculating some 3-color Ramsey numbers,
Technical Report of Gda´nsk University of Technology, ETI Faculty 18/03 (2003).
[8] Dzido T.: Multicolor Ramsey numbers...
Báo cáo toán học: "On-line Ramsey Theory for Bounded Degree Graphs" doc
... small on-line Ramsey numbers for paths and their generalization,
Australasian J. Combinatorics, 40 (2008), 27–36.
[22] P. Pralat, A note on off-diagonal small on-line Ramsey numbers for paths, Ars ... be H-coherent for some monotone additive family H, a family C contained
in C must somehow be “large enough”. In order to be A-plentiful for some H-strategy
A, the family C mu...
Báo cáo toán học: "On Some Non-Holonomic Sequences" pot
... holds, then {log n}
n
is not holonomic.
Proof. For distinct primes ρ
1
, ,ρ
s
,thenumberslogρ
1
, ,log ρ
s
are linearly indepen-
dent over Q, since for all c
1
, ,c
s
∈ Z we have
0=
s
i=1
c
i
log ... information we will need about W (z) can be found in [1].
Corollary 8. The Lambert W function is not holonomic.
the electronic journal of combinatorics 11 (2004), #R87 6
If a sequence of re...
Báo cáo toán học: "Chromatic Graphs, Ramsey Numbers and the Flexible Atom Conjecture" potx
... holds for k = 2 and k = 3. An interesting open
problem is whether equality holds for all values of k.
the electronic journal of combinatorics 15 (2008), #R49 2
Chromatic Graphs, Ramsey Numbers ... bound in claim 7 for P
1
as
an upper bound for the probability that condition (i) does not obtain for given xy ∈ E.
Since G has less than
3k − 4
k
2
edges, an upper bound for the...
Báo cáo toán học: "√ On Some Partitions Related to Q( 2)" ppsx
... the generating
function for χ
0
(n). The weight here being −1 raised to the number of parts of λ plus the
number of parts of µ. Now the next sum is the generating function for χ
2
(n) multiplied
by ... twice
the minimal part of µ.
Before proceeding to the next proof, we mention that the corollaries easily follow from
the lacunarity of the series involving indefinite quadratic forms. Furthe...
Báo cáo toán học: "On some densities in the set of permutations" ppsx
... O
1
k
(12)
uniformly in k 1 a nd x ∈ R.
Finally, we observe that these results can be used to obtain asymptotical formulas for
max
mk
d
k
(m) as k → ∞. We intend to discuss that in a forthcoming ... = k
1 + O(L
−1
)
.
In the last step we applied formula (14) and in the step before that we applied formula
(16). The derived expression for ϕ(ρ) also holds in the easier case ρ <...
Báo cáo toán học: "On multicolor Ramsey number of paths versus cycles" pdf
... P
6
, C
k
) = k + 2 for k ≥ 23,
(ii) R(P
6
, P
6
, C
k
) = R(P
4
, P
8
, C
k
) = k + 4 for k ≥ 27,
(iii) R(P
6
, P
7
, C
k
) = k + 4 for k ≥ 57.
3 Some three-color Ramsey numbers
In this section, ... to three-color Ramsey numbers for paths versus a cycle, see [3, 4, 5, 13].
In this paper, we provide the exact value of the Ramsey numbers R(P
n
1
, P
n
2
, . . . , P
n
t
,...
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