Báo cáo toán học: "LATIN SQUARES OF ORDER" potx

... 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-fac...

Ngày tải lên: 07/08/2014, 06:20

... coloring of K 2n,2n using the colors of the list at each edge. This paper will present the key lemma in the next section and then proceed to the proof of Theorem 5. We end with some discussions of ... Chessboard squares. Discrete Math. 141 (1995) 47–59. the electronic journal of combinat orics 13 (2006), #R47 8 Theorem 6 The list chromatic index of a bipartite graph equals the ma...

Ngày tải lên: 07/08/2014, 13:21

... 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

... 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 also another edge of ... journal of combinatorics 18 (2011), #P97 2 Two Characterizations of Hypercubes Juhani Nieminen, Matti Peltola and Pasi Ruotsalainen Department of Mathematics, University of Oulu...

Ngày tải lên: 08/08/2014, 14:23

... 1: Subsquares of N 2 squares of order 9. In particular we note that there are 1589 main classes of N ∞ squares of order 9, yet only 37 of these contain pan-Hamiltonian squares. In terms of reduced ... N 2 squares of order 4, we conclude that N 2 squares of order 9 cannot have proper subsquares except of order 3. The breakdown of the 1707 main classes according to...

Ngày tải lên: 07/08/2014, 06:20

... The set of partial latin squares of order n is denoted by PLS(n), and the set of latin squares of order n by LS(n). We say that P 1 ∈ PLS(n) contains P 2 ∈ PLS(n) if every filled cell of P 2 agrees ... question of which plexes are completable to latin squares. Following that is a section on the existence of plexes in Cayley tables of groups. Section 4 looks at plexes in la...

Ngày tải lên: 07/08/2014, 06:23

... each of which has a parallel class in one colour. The proof depends on the construction of a biembedding of a pair of Latin squares of side p, one of which has p 2 (p − 2)/8 subsquares of side ... biembeddings of Latin squares where paratopic copies are a llowed, and statements about particular realizations of Latin squares. For Latin squares A and A ′ with common set...

Ngày tải lên: 08/08/2014, 01:20

... is just the repetition of the proof of Lemma 3.2, we omit the details of its proof. With the aid of above preparations, now we will give the proof of Theorem 1.2. Proof of Theorem 1.2 By(1.8), ... similar to the proof of Lemma 3.1, so we omit the details of its proof. Lemma 3.4 Under the conditions of Theorem 1.2, F(x) satisfies the PS condition. Proof From the proof of Le...

Ngày tải lên: 20/06/2014, 21:20

... one-factorization of type 4 + 4 + 4 is only possible for three graphs of order 12: the disjoint union of three copies of C 4 , the disjoint union of three copies of K 4 ,and the union of K 4 and the ... properties of the classified one-factorizations are also tabulated. 1 Introduction An r-factor of a graph G is an r-regular spanning subgraph of G.Anr-factorization of G i...

Ngày tải lên: 07/08/2014, 08:22

... the tableau. Examine the content of the box to the right of the removed box and that of the box below of the removed box. Slide the box containing the smaller of these two numbers to the vacant position. ... (T 2 n ) † . Acknowledgments. The problem of combinatorial description of inclusion of orbital variety closures in terms of Young tableaux as well as the idea of the c...

Ngày tải lên: 07/08/2014, 08:22