Báo cáo toán học: "Two Characterizations of Hypercubes" potx

... journal of combinatorics 18 (2011), #P97 2 Two Characterizations of Hypercubes Juhani Nieminen, Matti Peltola and Pasi Ruotsalainen Department of Mathematics, University of Oulu University of Oulu, ... vertex of G has degree n i.e. G is regular of degree n. Claim 3.The graph G is bipartite. Proof of C l aim 3. If a prime convex P i cuts off an edge of a cycle it must cut off...

Ngày tải lên: 08/08/2014, 14:23

... spectrum of D a,b,0 (with δ  3). Lemma 3.4. The spectrum of D a,b,0 with δ = gcd(a, b)  3 consists of the eigenvalues of C δ (except 2 and −2) with multiplicity 3, the eigenvalues of C a and ... eigenvalues of C a ∪ C b and be of multiplicity 1. This ends the proof. From the above lemma we know to some extent the spectrum of D a,b,0 . If H is a tentative cospectral mate of...

Ngày tải lên: 08/08/2014, 12:22

... independent computations of the number of Latin squares of order 10. We also give counts of Latin rectangles with up to 10 columns, and estimates of the number of Latin squares of orders up to 15. Mathematics ... subgraph of degree one. A one-factorization of G is a partition of E(G) into one-factors. Clearly, the rows of a Latin rectangle R correspond to the one-factors...

Ngày tải lên: 07/08/2014, 06:20

... the members of i S [S] account for at least five of the seven nonempty subsets of S. Without losing generality we may assume that the complement in P(S) − {∅} of i S [S] is a subset of one of the following: (a) ... single member of S.Ifa (unique) member of S is of cardinality 1, then its unique element is considered to be a distin- guished vertex of G. The connectedness of...

Ngày tải lên: 07/08/2014, 06:20

Ngày tải lên: 05/08/2014, 15:20

... L. Sucheston, Convergence of classes of amart indexed by directed sets, Canad. J. Math. 32 (1980) 86–125. 13. U. Mosco, Convergence of convex sets and of solutions of variational inequalities, Adv. ... one-parameter discrete case, the notion of 1-mils coincides with the original notion of mils introduced by Talagrand [16]. The following lemma will be needed in the proof of the...

Ngày tải lên: 06/08/2014, 05:20

... respectively. The proof of this theorem follows the same line as in the proof of a very similar theorem formulated in [9, proof of Theorem 2.1]. 2.2. Embedded Formulas Efficiency of Embedded Explicit ... the f-evaluations of s components of the big vector F(t n e + h n c, Y n ) over a number of available processors. An additional computational effort consists of a recomputation...

Ngày tải lên: 06/08/2014, 05:20

... ⊆ ker(α) = 0, and so M is projective, as required. The proof of (5) ⇒ (1) is similar to that of (7) ⇒ (2) in Theorem 3.7. (7) ⇒ (1). By the proof of Proposition 2.3, every P -injective right R-module is ... Wakamatsu’s Lemma [6, Proposition 7.2.4]. Thus M is P -injective by the proof of (7) ⇒ (2).  New Characterizations and Generalizations of PP Rings 107 projective, as required....

Ngày tải lên: 06/08/2014, 05:20

... subgraphs of G;thus,toprove that G = G(T e ), it suffices to show Lemma 4 Each finite subgraph of G is contained in G 0 (T n ) for some n. Proof: It suffices to show that each edge of G belongs to one of ... incontractible, then G α is a multilink, and each component of T−α corresponds to a union of some of the bridges of the endpoints of e. If some such component, say T  , corr...

Ngày tải lên: 07/08/2014, 06:20

... part of the proof. An outline of the proof is given in the next section. The details are filled in in the subsequent sections. 2. Outline of the proofs of Theorems 1 and 2 Outline of the proof of ... in Theorem 1, so the proof of Theorem 1 is complete. The proof of Theorem 2 is given in Section 9. Analogously to the proof of The- orem 1, it is enough to count the rhombus tili...

Ngày tải lên: 07/08/2014, 06:20