Báo cáo toán học: "Maximum Multiplicity of Matching Polynomial Roots and Minimum Path Cover in General Graphs" ppsx

... Multiplicity of Matching Polynomial Roots and Minimum Path Cover in General Graphs Cheng Yeaw Ku Department of Mathematics, National University of Singapore, Singapore 117543 matkcy@nus.edu.sg Kok Bin ... Y. Ku and K. B. Wong, Maximum Multiplicity of a Root of the Matching Poly- nomial of a Tree and Minimum Path Cover, The Electronic Journal of C...

Ngày tải lên: 08/08/2014, 12:23

... condition for the maximum multiplicity of a root of t he matching polynomial of a tree to be equal to the minimum number of vertex disjoint paths needed to cover it. Before stating the main result, we require ... joined to at least two θ-essential vertices. the electronic journal of combinatorics 16 (2009), #R81 5 Maximum Multiplicity of a Root of the Matching Pol...

Ngày tải lên: 07/08/2014, 21:21

... contradiction. Finding the value of u 2 =sup{x ∈ S | x< 2 k } is the key point in determining the structure of S; u 2 will turn out to be the right end-point of the second component from the right in S. ... S and µ(S) are maximal) then S can be obtained by adding an end-point to each of the three disjoint open interval components of S k (3, 1). The proof is quite long, so w...

Ngày tải lên: 07/08/2014, 06:20

... set of positions of the nonzero entries in the generating vector of C. Then, for k ≥ 1, kS is the set of positions of the non zero entries in the generating vector of C k . Proof. The proof is ... matrices in C n attaining all the exponents in the interval [1, ⌊n/c⌋ + c − 2]. the electronic journal of combinatorics 16 (2009), #R66 2 Theorem 3.2 Let C ∈ C n and let S ⊆...

Ngày tải lên: 07/08/2014, 21:21

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 05/08/2014, 15:20

... station in Morrey spaces of the semilinear heat equations, J. Math. Sci. Univ. Tokyo 6 (1999) 793–822. 370 Jingshi Xu For readers interesting in standard Besov and Triebel-Lizorkin spaces and their ... {2 js ψ ∗ j,a f}  β (M p q )  the right side of (4), here the the first inequality is obvious, the second is (10) with Φ = Ψ,ϕ= ψ, and A and θ instead of Ψ and ψ in the...

Ngày tải lên: 06/08/2014, 05:20

... extending the classical results in finite-dimensional case obtained by Hinrichsen and Pritchard in [8]. The case of time-varying sys- tems has been considered in [9] and [3] where various formulas and ... A n ) −1 D i  . (26) The proof similar to that of Theorem 2.6 and is omitted. We note that the results obtained in Theorems 2.5 and 2.6 generalize results in [6] to m...

Ngày tải lên: 06/08/2014, 05:20

... are the numbers of the wires of the right outgoing lines of S k (X) in increasing order. The k-th row of Q(X), k ≥ 0, are the indices of the top outgoing lines of S k (X) in increasing order. As an ... y-coordinates of the right outgoing lines of the layers ordered increasingly (see Fig. 6). Assuming x 1 , ,x λ to be the x-coordinates of the top outgoing lines of the l...

Ngày tải lên: 07/08/2014, 06:22

... finite field has factors of distinct degrees, and the number of forests composed of trees of different sizes. Plan of the paper. We start by recalling in Section 1 the principles of two classical methods ... has implications in the determination of partial fraction expansions and symbolic integration, for instance. Most of the existing algorithms proceed by a reduction to...

Ngày tải lên: 07/08/2014, 13:21