Báo cáo toán học: "Evolutionary Families of Sets" potx

... S of subsets of a finite set S whose union is S is connected if and only if there is an evolutionary path in S between any two members of S. Proof:IfS is a finite connected family of subsets of ... 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...

Ngày tải lên: 07/08/2014, 06:20

... 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

... 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

Ngày tải lên: 05/08/2014, 09:46

Ngày tải lên: 05/08/2014, 15:20

... by Lunnon. No proof of Theorem 2.2 will be given because the proof of Theorem 2.2 is ex- tremely similar to the proof of Theorem 2.1 given below. 3 Proof of Theorem 2.1 For ease of notation let ... electronic journal of combinatorics 5(1998), #R3 12 4 Calculating the new upper bound Our first step is to construct the sequence of greatest elements of the given sequence of sets...

Ngày tải lên: 07/08/2014, 06:22

... the next operation of Type i. We proceed with an examination of each of the two phases before giving a formal definition of the distinction between the phases. For a clutch of operations in each ... least to within an additive constant, of the main result of [10]. They also showed that the size of a connected dominating set of an n-vertex cubic graph of girth at least 5 is...

Ngày tải lên: 07/08/2014, 06:23

... element A of its pedestal with the set of atoms dominated by A. In particular, we define the span S(F) of the pedestal to be the union of these sets of atoms, so S(F) is likewise a set of atoms of the ... number of isomorphism classes of m aximal intersecting k-uniform families of subsets of [m]. In this note w e prove the existence of a constant f (k) such that f(k,...

Ngày tải lên: 07/08/2014, 13:21

... family of subsets. The proof of Lemma 3.5 given in [4] can be easily modified to yield a similar result for G. For the convenience of the reader, we include the proof below. the electronic journal of ... the required shape as above.  Proof of Theorem 1.4 As before, the upper bound of |I| is given by the existence of Latin squares of order n 1 and Latin rectangles of order n...

Ngày tải lên: 07/08/2014, 15:22

... → u ′ then the hole of u ′ is contained in the hole of u, with the vertices of the former a subset of the vertices of the latter. Therefore, every triangulation of the hole of u ′ can be extended ... triangulation of the hole of u. Lemma 3.2. The number of i-vints (i ≥ 3) that charge a fixed 3-v i nt is at most C i−1 − C i−2 , and this bound is tight in the worst case. The...

Ngày tải lên: 08/08/2014, 14:22