Báo cáo toán học: "A note on the number of edges guaranteeing a C4 in Eulerian bipartite digraph" pot

... E}. Since no directed C 4 contains v ∗ as a vertex, we must have that every w ∈ A appears in at least one of A − or A + (it may appear in both; in particular, v ∗ appears in both A − and A + as there ... A note on the number of edges guaranteeing a C 4 in Eulerian bipartite digraphs Jian Shen Department of Mathematics Southwest Texas State Unive...

Ngày tải lên: 07/08/2014, 06:23

... the same way, an acyclic orientation on a fan graph induces an acyclic orientation on the corresponding comb graph. A simple adaptation of the last proof also gives a proof of the following the ... as mentioned before, the evaluation of the Tutte polynomial at these points is #P-hard for planar bipartite graphs [11] and even for grid graphs of maximum degree...

Ngày tải lên: 07/08/2014, 07:21

... types of input. Second, there are indications that increasing the training set of language processing tasks produces much larger performance gains than varying among algorithms at fixed training ... Task representation and evaluation method To formulate the task as a machine-learnable classi- fication task, we use a representation that encodes the joint task of chunking and func...

Ngày tải lên: 08/03/2014, 07:20

... left-maximal if, for every a ∈ Σ k ,thewordaw contains an abelian square subword beginning with the initial a. In particular, an abelian square-free word w is left-maximal over Σ k if aw contains an ... certainly contains a 3, two 4’s, two 5’s, two 6’s and a 7. It may also contain up to two 2’s, up to two additional 3’s, and an additional 7. Even if it contained all of these, how...

Ngày tải lên: 07/08/2014, 08:20

... simple proof of this last assertion, based on the decomposition of th e Laplacian of Cayley graphs, into a direct sum of irreducible representation matrices of the symmetric group. 1 Introduction If ... {1}, Z) the Cayley graph of G associated to the generating set Z. If A G is the adjacency matrix of G and ∆ G the corresponding Laplacian, since G is |Z|–regula...

Ngày tải lên: 07/08/2014, 21:21

... generating functions. Finally, in Section 6, we unify the main results of Sections 3, 4 and 5. We note that some of the results of t his paper have been announced in the 7 th Inter- national Conference ... distinction between these two not io ns. The le ngth |α| of a path α is the number of its steps. The height of a point of a path is its y-coordinate....

Ngày tải lên: 08/08/2014, 14:23

... Rassias, On the stability of the linear mapping in Banach spaces,” Proceedings of the American Mathematical Society, vol. 72, no. 2, pp. 297–300, 1978. 5 P. G ˘ avrut a, A generalization of ... M. Rassias, On the stability of functional equations and a problem of Ulam,” Acta Applicandae Mathematicae, vol. 62, no. 1, pp. 23–130, 2000. 16 Th. M. Rassias, Functional...

Ngày tải lên: 22/06/2014, 02:20

... proofs in [3] were based on expanding a permanent. It was pointed out by one of the r eferees that the transfer-matrix method gives a more direct and elegant proof of the generating function. ... 1 for the second transfer-matrix method, and that the matrix in the second transfer-matrix method is smallest possible for any transfer-matrix for this pro blem. the elect...

Ngày tải lên: 08/08/2014, 01:20

... the electronic journal of combinatorics 7 (2000), #R30 3 d (A) =gcd (A) ,d  (A) =d (A − A) , Λ (A) =maxA − minA, Λ  (A) =Λ (A) /d  (A) . Furthermore, let κ (A) = Λ  (A) − 1 |A| −2 ,θ (A) = max (A) Λ (A) , T ... Using an a ne transformation of variables his theorem can be stated as follows. Theorem 1. Let A be a finite set of integers and let h be a positive integer...

Ngày tải lên: 07/08/2014, 06:20

... paths that include the arc v n → v 1 , and there is a unique hamiltonian path of T that avoids this arc. Hence, there are 2 n−2 + 1 distinct hamiltonian paths in a nearly transitive tournament of order ... R. Proof. Note that we allow the special case where m = 0; in this case the path Q is a path on 0 vertices, and R = P satisfies the lemma trivially. The remainder...

Ngày tải lên: 07/08/2014, 13:21