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...

Ngày tải lên: 08/08/2014, 14:23

... 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 )...

Ngày tải lên: 07/08/2014, 15:23

... 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 =       ...

Ngày tải lên: 07/08/2014, 08:22

Ngày tải lên: 05/08/2014, 10:20

Ngày tải lên: 05/08/2014, 15:21

... 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...

Ngày tải lên: 07/08/2014, 06:20

... 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...

Ngày tải lên: 07/08/2014, 06:20

... 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...

Ngày tải lên: 07/08/2014, 07:21

... 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...

Ngày tải lên: 07/08/2014, 08:22

... 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...

Ngày tải lên: 07/08/2014, 08:22