Báo cáo toán học: "Another infinite sequence of dense triangle-free graphs" docx

... 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 in this sequence are 3- colourable. ... 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 sequence...

Ngày tải lên: 07/08/2014, 06:22

... design in the infinite family has the collection of five blocks mentioned above then so do all other members of the infinite family; 3) Give a design having the required collection of five blocks. Theorem ... matrix ofa2-(v, k, λ)designisab × v matrix A = a ij ,in which a ij =1ifblocki contains point j and a ij =0otherwise. 3 Results The strategy for establishing the existence of an...

Ngày tải lên: 07/08/2014, 06:20

... 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

... integer n. As a 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 ... derive the order of D + f from the number of solutions of y 2 = f(x). In particular, when y 2 = f(x) is in a certain class of elliptic curves, there is an explicit form...

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

... derivative of Z X (u) is a generating function for the number of circuits. See for instance [7]. Knowing the number of circuits of each length is sufficient to conclude the number of primitive circuits of ... 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 p...

Ngày tải lên: 08/08/2014, 12:22

... 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

... automorphism group of unitary Cayley graphs and answer the open question from [23] about the ratio of the size of the automorphism group of X n and the size of the group of a ffine automorphisms of X n . ... morphism group of a graph with square-f ree order and D = {1, p} is the wreath product of the group of class permutations C i and the groups of permutations of verti...

Ngày tải lên: 08/08/2014, 14:22

... 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 ... suffix of the Thue-Morse sequence t = 10010110 ···. The construction of this minimal sequence is given by an explicit algorithm. the electronic journal of combinatorics 5 (...

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