Báo cáo toán học: "On Kissing Numbers in Dimensions 32 to 128" pptx
Báo cáo toán học: "On Kissing Numbers in Dimensions 32 to 128" pptx
... 07 932- 0971, USA
Submitted: April 9, 1998; Accepted: April 13, 1998
ABSTRACT
An elementary construction using binary codes gives new record kissing numbers in dimensions
from 32 to 128.
1. Introduction
Let ... 1,260,230,400 in dimensions 32, 64 and 128, for example).
In contrast, Quebbemann’s lattice Q
32
[14], [5, Chap. 8] has τ = 261,120.
In recent years the kissing...
Báo cáo toán học: " On Score Sets in Tournaments" pptx
... 143–148.
3. J. W. Moon, Topics on Tournaments Halt, Rinehart and Winston, New York,
1968.
4. K. B. Reid and L. W. Beineke, Tournaments, Selected Topics in Graph Theory,
L.W. Beineke and R.J. Wilson, ... appeared in Chinese [6] in 1988 and in English [7] in 1989.
In the following result, we prove that any set of p non-negative integers
s
1
,s
2
, ,s
p
with s
1
<s
2
< < s
p...
Báo cáo toán học: "On regular factors in regular graphs with small radius" ppsx
... disjoint subsets D, S of V (G),
whether G has a k-factor or not.
In 1985, Enomoto, Jackson, Katerinis and Saito [3] proved the following result.
Lemma 2.2 Let G be a graph and k a positive integer ... eccentricity of vertices into
∗
corresponding author
the electronic journal of combinatorics 11 (2004), #R7 1
For regular graphs without a k-factor, for odd k, we can give the following result...
Báo cáo toán học: "On Directed Triangles in Digraphs" pps
... a useful consequence. In Section 3, we outline Shen’s proof of his
bound on α in [5]. In Sections 4 and 5 we prove Theorem 2. In Section 6 we outline a
part of the proof in [4] and prove Theorem ... so that the
resulting digraph D
is acyclic.
If true, this conjecture would imply the following strengthening of Lemma 5: Each
digraph D obtained from a tournament by deleting k edges,...
Báo cáo toán học: "On identifying codes in the king grid that are robust against edge deletions" potx
... two
non-codewords in F(i, j) are in the lower-left and upper-right corners (in the other case,
we just go up instead of going down in what follows: as explained above, the voting rule
is symmetric in this ... identifying codes in graphs, Information
Processing Lett., 102 (2007), pp. 92–98.
the electronic journal of combinatorics 15 (2008), #R3 12
2 Unknown edge deletions
We begin b...
Báo cáo toán học: "On unimodality problems in Pascal’s triangle" potx
... It is natural to ask for a combinatorial interpretation. Lattice
path techniques have been shown to be useful in solving the unimodality problem. As an
example, we present a combinatorial proof ... Q
1
, Q
2
into three subpaths q
1
, q
2
, q
3
. Let p
1
be obtained by moving p
1
down to Q
1
south δ−d units
and p
3
be obtained by moving p
3
right to Q
2
east δ units. Then we obta...
Báo cáo toán học: "On winning fast in Avoider-Enforcer games" pps
... hope
is to determine not only the winner of a game, but also how fast is he able to win.
For a game F, let τ
E
(F) be the smallest integer t such that Enforcer ha s a strategy to
win the game F in ... later
Hefetz et al. [7] studied the fast winning in Maker-Breaker Hamiltonicity game.
We would like to emphasize that, generally speaking, results on fast winning in po-
sitional g...
Báo cáo toán học: "On some densities in the set of permutations" ppsx
... O(L
−1
).
Inserting this expression into the previous equality and integrating we obtain the desired
result (10).
To prove (11 ) , we first restrict the region to 1 k
√
m where all obtained remainder
term ... 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 paper.
2 The s...
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