Báo cáo toán học: "Characteristic polynomials of skew-adjacency matrices of oriented graphs" pdf

... ···, 1 λ n i} for the skew-adjacency matrix of −→ T −1 is the inverse of the skew-adjacency matrix of −→ T and the negative of each eigenvalue of T is also an eigenvalue of T. Therefore Sp( −→ T −1 ) ... number of edges oriented in the direction of the routing. Otherwise C is oddly oriented. Let S = (s ij ) be skew-adjacency matrix of an oriented graph G σ . Note...

Ngày tải lên: 08/08/2014, 14:23

... call a subset D ⊆ E of the set of arcs E a transversal of the family of oriented cycles of  G if D intersects all oriented cycles of  G.Fromnowon,bya transversal in an oriented graph  G, we ... mean a transversal of the family of oriented cycles of  G. A dual version of Woodall’s conjecture may be stated as follows: for any planar oriented graph  G, the ori...

Ngày tải lên: 07/08/2014, 07:21

... both made up only of vertices of degree two in Γ. 2.4 A refined analysis of the degrees in Γ Let us further partition the sets X and B:letC  2 and C  3 be the subsets of X with vertices of degree two ... one I-set of cardinality at least three. Thus, C  is the set of all codewords belonging only to I-sets of size one or two. Our strategy will be to bound  ≥3 from below by a...

Ngày tải lên: 07/08/2014, 06:20

... space of dimension  r + p − 2 p − 1  +1 of polynomials of form Q + α,whereQ is an r-variable homogeneous polynomial of degree p − 1andα ∈GF p . (To prove this without the triangle criterion of ... and its rank is at most k 2c √ k . Due to the choice of k the statement follows. The proof of Theorem 9 follows the same steps as the proof of Theorem 8. If m has  prime divisor...

Ngày tải lên: 07/08/2014, 06:20

... number of disjoint bent paths necessary to cover such a grid. We call a set of vertex-disjoint bent paths that include all vertices a bent path covering.Thesize of such a covering is the number of ... restricted types of Hamilton paths and cycles in grids; one that does is the paper of Trotter and Erd¨os [6] about the existence of directed Hamilton cycles in the Cartesian produc...

Ngày tải lên: 07/08/2014, 07:21

... matching. Proof of Theorem 1.3. Let T and F be as in Theorem 3.2. Let G consist of those elements of F belonging to the range of F , and let H = F \ G. For every t in T let J t be a perfect matching of ... G ∗ i ), let S i be the set of vertices s of G ∗ i for which there is an M ∗ i -alternating X i − s path of odd length in G ∗ i , and let T i be the set of vertices t of...

Ngày tải lên: 07/08/2014, 21:21

Ngày tải lên: 05/08/2014, 09:46

... electronic journal of combinatorics 12 (2005), #N4 6 Chain polynomials of distributive lattices are 75 % unimodal Anders Bj¨orner Department of Mathematics Royal Institute of Technology S-100 ... c i of chains of length i in the proper part L \{0, 1} of a distributive lattice L of length  + 2 satisfy the inequalities c 0 < <c /2 and c 3/4 > >c  . This pro...

Ngày tải lên: 07/08/2014, 08:22

... extension of the decomposition of derangements given by Kim and Zeng [11] in their combinatorial proof of (1.3). Combinatorial Proof of Theorem 3.3. First, we give an outline of the proof of Kim ... number of type B weak excedances of σ. In view of the above definition of type B excedances, we can define a type B analogue of the derangement polynomials. Definition 2.2 The...

Ngày tải lên: 08/08/2014, 01:20

... d). Thus the set of characteristic points of the system forms an antichain under the partial ordering ≤. Proof. For the proof assume, in view of Remark 8, that all second partials of the G i with respect ... a i , 1 ≤ i ≤ k. Proof. This is a special case of Hille’s law of permanence for functional equations given in §10 .7 of Vol. 2, [11]. B.3 The Perron-Frobenius theory of no...

Ngày tải lên: 08/08/2014, 12:22