Báo cáo toán học: "The quantifier semigroup for bipartite graph" pot
Báo cáo toán học: "The quantifier semigroup for bipartite graph" pot
... y: w ≤ w
′
if wS ⊆ w
′
S for all G a nd all S ⊆ U.
The focus of this paper is the partial order on the following semigroup:
Definition 2. The quantifier semigroup for bipartite graphs, S, is defined ... can easily identify
the electronic journal of combinatorics 18 (2011), #P123 7
The quantifier semigroup for bipartite graphs
Leonard J. Schulman
∗
Submitted: Jun 22, 2010; Acce...
Báo cáo toán học: "The IC-Indices of Complete Bipartite Graphs" potx
... true for
m = n = 2. So, assume that n ≥ 3. By Proposition 3.3, we may let f(u
i
) < f(u
i+1
)
for i ∈ [1, m + n − 1]. For convenience of calculation, we also let f
i
=
i
=1
f(u
) for
i ... 2
n
− 1 and (2) M(K
1,n
) = 2
n
+ 2 for all n ≥ 2. Then,
in 2005, Salehi et al proved that M(K
2,n
) = 3 · 2
n
+ 1 for n ≥ 2 [13]. In this paper, we
prove that for 2 ≤ m ≤ n, M(K
m,n
)...
Báo cáo toán học: " The Redheffer matrix of a partially ordered se" doc
... at
once from the formula for finding the inverse of a matrix that differs from one of known
the electronic journal of combinatorics 11(2) (2004), #R10 3
inversebyamatrixofrank1.Theformulais
(B + ... closely connected to the Riemann Hy-
pothesis (RH). Let R
n
be the n ×n matrix whose (i, j) entry is 1 if i|j or if j =1,and
otherwise is 0, for 1 ≤ i, j ≤ n. For example,
R
8
=
...
Báo cáo toán học: "The size of Fulton’s essential set" pot
... really nice formula known for v
n
. However, J. West has
proved the formula v
n
=
|λ|=n,l(λ)≤3
(f
λ
)
2
; the interested reader is refered to Mac-
donald [5, p. 22], where the above formula, combined ... certitude.
Conjecture 3.12 For fixed integer k ≥ 2 and variable n, the coefficient of x
n−k
in
V
n
(x) can be expressed as a polynomial in n of degree k −2.
We have been able to prove this...
Báo cáo toán học: "The Gr¨tzsch Theorem for the hypergraph of o maximal cliques" pdf
... uses both colors on K. Therefore, c is a 2-coloring of H(G).
For the skeptics of the proof of the 4-Color Theorem and since we do not
want to use this powerful theorem for our application if not ... assume henceforth.
Suppose that a vertex v ∈ V (G)\V (C) has two neighbors x
i
, x
j
on C
which are not consecutive vertices of C.Sincek≤7, there is a color a ∈ L(v)
such that a = c(x) for a...
Báo cáo toán học: "The Neighborhood Characteristic Parameter for Graphs" pptx
... overcounting is corrected for in the following theorem (which also
shows that, for a bipartite graph G,
N char(G) equals twice the bipartite characteristic’
defined in [5]).
Theorem 1 For every graph G ... char(H)=2.
Conversely, suppose G is not chordal bipartite. If G is not bipartite, then G contains
an induced odd cycle C and
N char(C)=0. IfG is bipartite but not chordal bipar...
Báo cáo toán học: "The Tur´n problem for hypergraphs of fixed size " ppsx
... a forest of given size.
Lemma 2 (i) An r-uniform hypergraph with at least r!(t − 1)
r
edges contains a forest
with t edges.
(ii) Let F be a 3-uniform hypergraph. Then either (a) F contains a forest ... [5] conjectured that for any t there is a
constant C so that any r-uniform hypergraph with C
r
edges contains a sunflower with t
edges. We can obtain a bound of this form for forests, indeed...
Báo cáo toán học: "The Edmonds-Gallai Decomposition for the k-Piece Packing Problem" potx
... maximum weight bases
of M with the weight function X → | X| for X ∈ π. This weighted matroidal approach
yields a proof for the Berge-type formula of [5] on the size of a maximum k-piece packing.
Indeed, ... one can see that all the above considerations for the k-piece packings hold
for the (l, u)-piece packings as well, with the necessary modifications. For illustrating this,
we bri...
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