Báo cáo toán học: "The lonely runner with seven runners" pdf
Báo cáo toán học: "The lonely runner with seven runners" pdf
... 1/(k + 1) along the track to every
other runner. The lonely runner conjecture states that every runner gets lonely.
The conjecture has been proved up to six runners (k ≤ 5). A formulation of the
problem ... case of the conjecture with
seven runners.
1 Introduction
Consider k + 1 runners on a unit length circular track. All the runners start at the same
time and place and each ru...
Báo cáo toán học: "The independence number of graphs with large odd girth" ppt
... independent sets in graphs with large odd girth at. To illustrate the ideas
behind this algorithm we shall first prove our results for graphs of odd girth at least
7. Dealing with graphs with larger odd ... .
The results of this paper are designed to deal with the case when the average
degree of the graph is large. We shall prove that an r-regular graph without 3 and
5 cycles has an in...
Báo cáo toán học: "THE INDEPENDENCE NUMBER OF DENSE GRAPHS WITH LARGE ODD GIRTH" ppsx
... 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 1 (1994) #R9.
2
We can now prove the ... ≥
v∈G
1
2
(1 + d
1
(v)+···+ d
k−1
(v))
1+d
1
(v)+···+ 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 ve...
Báo cáo toán học: "The Fraction of Subspaces of GF(q)n with a Specified Number of Minimal Weight Vectors is Asymptotically Poisson" pot
... number of ordered
bases, the fraction of ordered bases with a desired property will be the same as
the fraction of d-dimensional subspaces with the property. We will look at ordered
bases.
The ... remainder of the paper, and GF(q)be
the finite field with q elements. Because the underlying field is finite, there are
many counting problems associated with fundamental concepts of linear alge...
Báo cáo toán học: "The asymptotic number of set partitions with unequal block sizes" pot
... contrasts sharply with the present topic of partitions
with distinct block sizes. In this case, we show that a typical partition has blocks of sizes
1, 2, ,s, where s is approximately
√
2n, with a few ... ∈ Π(n, r)withh
i
=h
i
+1 = x, h
j
= h
j
−1=y,and
h
t
=h
t
for all other t.ThenP(π
)>P(π). Therefore the π ∈ Π(n, r) which maximizes
P (π) cannot have two integers x and y w...
Báo cáo toán học: "The order of monochromatic subgraphs with a given minimum degree" doc
... the edges of G with two colors there is a
monochromatic subgraph with minimum degree at least d and order at least t.Let
f
G
(d) = 0 in case there is a 2-coloring of the edges of G with no such ... its
edges with the color i.IneachA
i
we place a (d −1)-degenerate graph with the maximum
possible number of vertices of degree 2(d − 1). It is easy to show that such graphs exists
with...
Báo cáo toán học: "The Structure of Maximum Subsets of {1, . . . , n} with No Solutions to a + b = kc" potx
... s
B
<l
1
with C as in (I) we can verify that, for
sufficiently large n,
C ⊆
2r
1
− ξ
1
− kξ
2
− 2k
2
+ k − 5
2
,r
1
⊆ (l
1
,r
1
],
|C \ A| > |B| and max K<s
C
. By analogy with part ... by compar-
ing A
3
with A
2
that almost the whole interval (l
3
,r
3
]mustbeinA. Having achieved
this, we infer by Lemma 1 that (r
3
,l
2
] ∩ A is nearly empty. Comparing A
2
with A
1
will
t...
Báo cáo toán học: "The maximum number of perfect matchings in graphs with a given degree sequence" docx
... the
same edge taken twice), where each such H is counted 2
s
times, with s being the number
of components (that is, cycles) of H with more than 2 vertices. Indeed, every union of a
pair of perfect ... as
well. Here, too, each such H
is counted 2
s
times, where s is the number of cycles of H
with more than 2 vertices, (as there are 2 ways to orient each such cycle as a directed
cycle...
![Báo cáo toán học: " The Number of [Old-Time] Basketball Games with Final Score n:n where the Home Team was never losing but also never ahead by more than w Point" pot](https://media.store123doc.com/images/document/2014_08/07/medium_fbh1407399746.jpg)
Báo cáo toán học: " The Number of [Old-Time] Basketball Games with Final Score n:n where the Home Team was never losing but also never ahead by more than w Point" pot
... begin with either the (1, 1) or (2, 2) step and end with either the (1, −1) or
(2, −2) step. If the walk starts with (1, 1) and ends with (1, −1), then there could be an
arbitrary [00] walk with ... between. If the walk starts with (1, 1) and ends
with (2, −2), there has to be an arbitrary [01] walk with width w − 1 in between. If the
walk starts with (2, 2) and ends with...
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