Báo cáo toán học: "Long path lemma concerning connectivity and independence number" pdf
Báo cáo toán học: "Long path lemma concerning connectivity and independence number" pdf
... other standard notation comes
from [1].
the electronic journal of combinatorics 18 (2011), #P149 2
Long path lemma concerning connectivity
and independence number
Shinya Fujita
∗
Alexander Halperin
†
Colton ... theorem and, following the proofs presented in [4], we prove the
following lemma which is o ur main result.
Lemma 1 Let k ≥ 1 be an integer and let G be a g raph of...
Báo cáo toán học: "Pattern avoidance in permutations: linear and cyclic orders" pdf
... escalating Dyck path, and the action of the first-return
and the sink-or-float bijections.
643125
12
789643125
312467958
a) b)
2 Dyck paths and classical permutation avoidance
A panoramic Dyck path of ... a
1
<a
2
and a
3
<a
4
(note that s
3
and s
4
belong to
the same horizontal edge); since there are at least two long horizontal edges and s
2
and
s
3
belong respectively...
Báo cáo toán học: "On a conjecture concerning dyadic oriented matroids" pptx
... (1999), #R23 5
matroid, we apply Proposition 1 and conclude that A
k
and A
k
are equivalent repre-
sentations of M
k
. Each representation is in standard form with respect to the same
base, so ... follows:
(D
k
)
ij
=
1, if j =1;
1, if i = j − 1andj≥2;
2, if j = 2 and i ≥ 2;
2, if i = j =2k+2;
−1, if i ≥ j and 3 ≤ j ≤ 2k +1;
0, otherwise.
Let e
1
,e
2
,...
Báo cáo toán học: " Long heterochromatic paths in edge-colored graphs" potx
... = s,andifx = l − s +3 and x
= s +1, then
x − s +2=l − s +3− s − 2=l − 2s +5=s +1. So,if4≤ x
≤ x − s +2,thenx
≤ s
and hence x
+(x − s) − 1 ≤ x − 1, and so P
is a heterochromatic path ... 10l +7 ifs ≤ 2l − k − 1andk ≡ 1, 4(mod 5);
6k − 10l +10 if s ≤ 2l − k − 2andk ≡ 2(mod 5);
2ifs =2l − k and k ≡ 1, 4(mod 5);
1ifs =2l − k or s =2l − k − 1andk ≡ 2(mod 5),
≥ 1
and x
− (x...
Báo cáo toán học: "Kocay’s lemma, Whitney’s theorem, and some polynomial invariant reconstruction problems" docx
... <v(G)andv(Y ) <v(G). Now
2G
F
=
2H
F
follows from the fact
that G and H have identical vertex decks and Kelly’s Lemma.
The following corollary is an immediate consequence of the above lemma.
Corollary ... to G.
1. When F
2
=2G, then Equation (10) follows from Lemma 2.9 and Corollary 2.10.
2. When F
1
= G + X and F
2
= G + Y ,andv(X) <v(G)andv(Y ) <v(G), we ha...
Báo cáo toán học: "On a conjecture concerning the Petersen graph" ppt
... he path is called a short overpath
and in the second, a long overpath. Note that both long and short overpaths may use
monobridges.
(In Figure 4.1, P
1,3
denotes a short {x
1
, x
3
} overpath and ... overpath gives rise to both a short {x
i
, x
i+2
} overpath and a
short {x
i+1
, x
i+3
} overpath via a suitable selection of an edge joining x
i+1
and N
′
i+1
and an edge joining x...
Báo cáo toán học: "Lattice path proofs of extended Bressoud-Wei and Koike skew Schur function identities" pdf
... 21-34.
[3] I.M. Gessel and X. Viennot, “Binomial determinants, paths, and hook length formu-
lae”, Adv. Math 58 (1985), 300-321.
[4] I.M. Gessel and X. Viennot, “Determinants, paths, and plane partitions”, ... subscripts i and j of h
i
(x) and h
j
(y) determine the number of horizontal steps east
and west, respectively, o f the corresponding lattice paths. The north-east paths P...
Tài liệu Báo cáo khoa học: Long-distance interactions between enhancers and promoters The case of the Abd-B domain of the Drosophila bithorax complex pdf
... is thought to
be active, while the other three are silenced. In A6, both
iab-5 and iab-6 are active, and iab-7 and iab-8 are
silenced, but only iab-6 drives the expression of Abd-B.
Similarly, ... avoid other pro-
moters, and to locate and physically approach their
proper target promoter in the viscous environment of
the nucleus.
Somatic pairing of chromosomes and
the regulation o...
Báo cáo toán học: " Optimized spectrum sensing algorithms for cognitive LTE femtocells" pdf
... of macrocells and femtocells.
2- Self-optimization and auto-configuration: The
femtocell is expected to operate in a plug and play
fashion to ease installation, conf igurat ion, and man-
agement. ... Gaussian independent
and identically distributed (i.i.d.) random variables with
zero mean and variance s
2
. In channel sensing, we are
interested in the probability of detection, P
d...
Báo cáo toán học: " EURASIP Journal on Wireless Communications and Networking" potx
... values of
D
RSU
would lead to longer multi-hop paths, in terms
of number of traversed nodes, and therefore lower
effective bandwidths. Only for R = 150 m and in
the motorway scenario (this behavior ... forwarding within an
area, and affected protocol layers.
Figure 3: Geographical area partitioning and
IPv6 virtual link abstraction.
Figure 4: Multi-hop connectivity between a car
and...
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