Báo cáo toán học: "A note on polynomials and f -factors of graphs" docx
Báo cáo toán học: "A note on polynomials and f -factors of graphs" docx
... mind, we define a partial f- factor of a graph G = (V, E) to be an
˜
f- factor of
G where
˜
f( v) = f( v) ∪ {0} for all v ∈ V , and a partial f- factor of G is non-trivial if it is
non-empty. Our next result ... sufficient condition for the existence of an f- factor of G. No necessary and
sufficient condition for an f- factor exists when we allow |f( v)| ≥ 2, even when |f( v)|...
Báo cáo toán học: "A note on the non-colorability threshold of a random graph" pot
... f
2
(α, y)lnf
2
(α, y)
and
−β
1
0
ln(
f
3
(β,1 − x − y) − t
1 − t
)dt − f
3
(β,1 − x − y)lnf
3
(β,1 − x − y)
This completes the proof of the convexity of ln E as a function of (α, β, x, ... (3)
When conditioning on the event C
P
0
, the random graphs of the resulting probability
space may contain edges only from within the edges that connect vertices of differen...
Báo cáo toán học: "A note on the distance-balanced property of generalized Petersen graphs" ppt
... positive answer to Conjecture 1.
2 The Proof of Theorem 2
First we give a direct observation.
Proposition 3 For any i = 0, 1, 2, , n − 1, d(u
0
, u
i
) − d(v
0
, u
i
) = 1 if and only i f there
exists ... 0}, and
W
vu
= {x ∈ V (G) | d(v, x) − d(u, x) = −1} form a partition of V (G). The following
proposition follows immediately from the above comments.
Proposition 1 If |W
uv
| >...
Báo cáo toán học: " A note on the almost sure limit theorem for self-normalized partial sums of random variables in the domain of attraction of the normal law" pptx
... Sponsor Teams for Innovation in the
Construction of Talent Highlands in Guangxi Institutions of Higher Learning ([2011]47), and the support program of
Key Laboratory of Spatial Information and ... ε
0
< 1 in theorem 1.1 of [12].
Remark 1.4. If EX
2
< ∞, then X is in the domain of attraction of the normal law. Therefore, the class of random
variables in Theorems 1.1 i...
Báo cáo toán học: "A Note on Maximal Nonhamiltonian Burkard–Hammer Graphs" pptx
... satisfies the Burkard–
Hammer condition;
(ii) If |I| = 5and G satisfies the Burkard–Hammer condition, then G has no
Hamilton cycles i f and only if G is isomorphic to one of t he graphs H
1,n
,
H
2,n
, ... ∅,B
2
(H
t
) = ∅ and B
1
(H
t
) = ∅.
The proof of Lemma 4 is complete.
ProofofTheorem9.
(a) Let k = 4. Then the graph L = S(I(L) ∪ K(L),E(L)) of Lemma 2 is a
maximal nonhamil...
Báo cáo toán học: "A note on antichains of words" potx
... a prefix of m
i
, f( a)isaprefixofm
j
. Thus l and f( a) are both prefixes of m
j
,
and one must be a prefix of the other. Since a is an internal subword of m
i
, f( a)isaninternal
subword of m
j
. ... m
j
is overlap-free.
Since aab is a prefix of m
i
,f( aab)=aaf(b)isaprefixofm
j
. However, another prefix of
m
j
is aabaab. Thus one of f (b)andbaab is a prefix of the other...
Báo cáo toán học: "A Note on the Symmetric Powers of the Standard Representation of Sn" ppt
... 8
Proposition 3.3. There exists a constant c>0 such that
H(n) ≥
n
2
2
−cn
3/2
for all n ≥ 1.
Proof. From the definition of H(n) and Proposition 3.2 (and the fact that the
right-hand side of equation ... have:
Proposition 1.2. dim F
n
= D(n).
Proof. Consider the table of the characters χ
N
; we are interested in the dimension
of the row-span of this table. Since the dimension...
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