... A simple algorithm for constructing
Szemer´edi’s Regularity Partition
Alan Frieze
Department of Mathematical Sciences,
Carnegie ... combinatorics 6 (1999), #R17 3
A partition satisfying the second criterion is called equitable. V
0
is called the
exceptional class.
Following [9], for every equitable partition P into k +1classes ... (ˆx
+
)
T
Wˆy
−
≥ ˆγ
√
pq/4. (The proof
for...
... September 20, 1996).
[3] P.K. Wong. Cages - a survey, JournalofGraphTheory,6, 1982, 1-22.
A Simple Method for Constructing Small Cubic Graphs of Girths
14, 15, and 16
Geoffrey Exoo
Department of Mathematics ... 26, 1996
Abstract
A method for constructing cubic graphs with girths in the range 13 to 16 is described. The
method is used to construct the smallest known cubic graphs for...
... only if e(i)=e(j) for all i, j.
In [11], Wagner and West conjectured that exponentially balanced Gray codes exist
for all length n. By extending the method of Robinson and Cohn for the construction ... based on Bakos’s construction of
Gray codes in [1] which was reformulated in a simple way by Knuth in [4, Theorem D].
This proof is much simpler than the one given in [10].
In the seque...
... according to Lemma 1.
2. Suppose that a comes from a fork. Since deg(o) = 4 , o must be the white node
in the fork. Then d is also contained in the same fork. Hence, no de 4 must have
degree one. This ... following cases:
1. Suppose that a comes from a fork. Since the degree of o is 4, o must be the white
node in the fork. Thus, f is contained in the same fork. Then node 4 must have
degree 1,...
... the ring of formal power series in
x over Q. We introduce an Eulerian differential operator δ
x
in x by
δ
x
(f(x)) =
f(qx) − f(x)
qx − x
,
for any f (x) ∈ Q[q][[x]] in the ring of formal power ... A recurrence relation for the “inv” analogue of
q-Eulerian polynomials
Chak-On Chow
Department of Mathematics and Information Technology,
Hong Kong Institute of Education,
10 ... degree n. Any el...
... of Garsia-
Haiman modules when q = 0. This is true for any general shape of µ. Based on (2.3), the
combinatorial formula for the Hilbert series for the two column case was constructed by
Garsia ... ∈SYT(µ
′
)
n
i=1
[a
i
(T )]
t
, (6.2)
when q = 0. Since (2.2) is true for general shape o f µ, by (6.1 ) , the Hilbert series of M
µ
for any shape of µ would have the form in (6 .2 ) wh...
... can see that (1) for CD and
the initial part of (2) for BD will follow from (3) for ABCD. So we will concentrate on
the validity of (3) for ABCD, and the latter part of (2) for BD, i.e., the ... sense.
Since the claims already hold for segments and cells contained in I
1
, the new claims to be
proved are the claims (1) for the segment CD, (2) for the segment BD, and (3) for...
... problem of (sometimes simple) undirected graphs with
given degree sequences even admits simple greedy algorithms for its solution.
Subsequently, the theory was extended for factor problems of ... Havel developed a simple greedy algorithm
to solve the degree sequence problem for simple undirected graphs ([8]). In 1 960 P. Erd˝os
and T. Gallai studied the f-factor problem for t...
...
Hamaguchi's hardware algorithm (Ham~guchi,
1988), proposed for speech recognition
systems,
is
similax to Fukushima's algorithm. In Hamaguchi's
algorithm, S bit memory space ... the
worst case time complexity for sequential mor-
pheme extraction algorithms is
O(MN).
On
the other hand, the above proposed algorithm
(Fukushima's algorithm) has the advanta...
... compare SIMR's performance on these language
pairs to the performance of other algorithms, Table 2
shows that the performance on other language pairs
is no worse than performance on French/English. ...
was 5.7 characters. Church's
char_align
algorithm
(Church, 1993) is the only algorithm that does not
use sentence boundary information for which com-
parable results hav...