Báo cáo toán học: "An infinite family of non-embeddable Hadamard designs" potx

... = λ+1 3 T 6 = { 5λ+5 3 , 5λ+8 3 , , 2λ +1} then |T 6 | = λ+1 3 An infinite family of non-embeddable Hadamard designs K. Mackenzie-Fleming Department of Mathematics, Central Michigan University Mount Pleasant ... existence of an infinite family of non-embeddable 2 - (2λ +2,λ +1,λ)designs,λ = 3(2 m ) − 1,m ≥ 1 is established. Mathematical Reviews Subject Number: 05B05 Dedica...

Ngày tải lên: 07/08/2014, 06:20

... 05C38 Abstract In 2009, Cooper presented an infinite family of pairs of graphs which were con- jectured to have the same Ihara zeta function. We give a proof of this result by using generating functions ... demonstrate add itional families of pairs of graphs which share the same zeta function. 1. Introduction In 2009 , Cooper described an infinite family of non-isomorphic pa...

Ngày tải lên: 08/08/2014, 12:22

... partially ordered set of finite permutations ordered by deletion of entries contains an infinite antichain. In other words, there exists an infinite collection of permutations no one of which contains ... than the poset of graphs ordered by the operations of edge contraction and vertex deletion. (That this poset of graphs does not contain an infinite antichain is a famous theo...

Ngày tải lên: 07/08/2014, 06:20

... structural properties and that the natural way to describe the structure of these graphs is in terms of graph homomorphisms. One infinite sequence of cores of dense maximal triangle-free graphs was known. All graphs ... 4-colourable, in contrast to a conjecture of Jin [8], saying that there are graphs of arbitrarily large chromatic number with this property. Another infinite seq...

Ngày tải lên: 07/08/2014, 06:22

... consequence, we obtain new infinite families of 3-designs. In particular, we get infinite family of 3-designs whose block size is congruent to 1 modulo p. 2 Zero sets of algebraic curves Let p be ... of X is contained in precisely λ blocks. For general facts and recent results on t-designs, see [1]. There are several ways to construct family of 3-designs, one of them is to u...

Ngày tải lên: 07/08/2014, 15:22

... accumulation vertices of degree 6. Proof. Figure 6 illustrates a construction of a plane graph F 1 that fulfills all conditions of the definition of a plane 13-belt graph except (B1). Splitting of a vertex ... communication and preprint of [2]) that typi- cal constructions of infinite families of simple 3-connected k-crossing-critical graphs create bounded numbers (wrt. k) of...

Ngày tải lên: 07/08/2014, 21:20

... prefix of x of length 5. Proof. Firstnotethatthewordyis necessarily overlap-free by assertion 1 of Lemma 2. The existence of the decomposition for finite words is proved in [10], in the proof of Theorem ... this factorization of x,thewordu(resp. v) depends only on the prefix (resp. suffix) of x of length 7. This is recalled in the following table of all possible prefixes (resp. su...

Ngày tải lên: 07/08/2014, 06:22

... a tree. Proof: It suffices to prove that every edge of T (G) is an isthmus. Corollary 9 shows that if [x, y] is any hinge of G, then the cleavage units of G are precisely the cleavage units of the ... of K,oneofH and J is 2-connected. It is straightforward to show the corresponding one of H  and J  is also 2-connected, so that (H  ,J  ) is a hinge-separation of G. But then eve...

Ngày tải lên: 07/08/2014, 08:20

... the infinite hypercube Q of dimension is defined as the Cartesian product of copies of K 2 . Its vertex set is the set of all functions of a set S of cardinality into {0, 1}, where the preimage of ... an infinite graph of bounded, finite degree and G contains a one-way infinite isometric path R. Let u 0 be the first vertex of R, and label all vertices of R with ∆, where ∆...

Ngày tải lên: 07/08/2014, 15:22

... If S is a subspace of L(∆, α), then S consists of all hyperplanes of α which contain a given subspace β of α. Then S, regarded as set of lines of ∆, consists of all lines of ∆ through α contained ... point-line geometry: (i) P is the set of all partitions of A in n + 1 subsets of size 2; (ii) L is the set of all partitions of A in n − 1 subsets of size 2 and one su...

Ngày tải lên: 07/08/2014, 21:21