Báo cáo toán học: " Independence number and disjoint theta graphs" doc

... Chvatalova and J. Opatrn ´y. The bandwidth of theta graphs. Utilitas Math., 33:9–22, 1988. [12] Y. Egawa, H. Enomoto, S. Jendrol, K. Ota , and I. Schiermeyer. Independence number and vertex -disjoint ... T i for some i. Let u and v be the hub vertices of T and let Q 1 , Q 2 and Q 3 be the paths of T ea ch containing u and v. Suppose u and v are each incident to at least...

Ngày tải lên: 08/08/2014, 14:23

... pure two-dimensional and has only eight maximal faces. The case k = 3 is handled at the end of this section. Let k ≥ 4 and let Q k denote the face poset of Ind(SG 2,k ) and let I k+2 be a (k ... even numbers or the odd numbers; and M: We say X is a middle vertex for all other cases. {3,5,7,9} {1,3,5,7} {2,4,6,8} {4,6,8,10} {2,4,6,9} {1,4,6,9} {3,5,7,10} Figure 1: SG 4,2 Figures 1 and...

Ngày tải lên: 08/08/2014, 14:23

... separability and Schurity numbers of cellular algebras and schemes and study general properties of them. Sections 5 and 7 are devoted to computing the separability and Schurity numbers for 3/2- homogeneous ... called the separability number and the Schurity number of W respectively. The separability number s(C) and the Schurity number t(C) of a scheme C are defined as the...

Ngày tải lên: 07/08/2014, 06:20

... =  x∈S N G (x). If A and B are sets, then A − B = {a ∈ A: a /∈ B}. 2 Independence ratio at least 1/4 The independence number of a graph is the sum of the independence numbers of its components. ... (2009), #R27 2 Since f(z 3 ) = 3 and f(u 1 ) = 1, we have f(u 2 ) = 2, and then f(u 3 ) = 3. Now f(x 1 ) = 1 and f(u 3 ) = 3 imply f(ˆy 2 ) = 2, and hence f(ˆy 3 ) = 3 and f(ˆy...

Ngày tải lên: 07/08/2014, 21:21

... combinatorial Alexander duals of Ind(G) and EC(G) respectively. This and the Alexander duality provide us with isomorphisms of homology groups of Ind(G) and EC(G) in appropriately shifted and restricted ... (G)| and m = |E(G)| so that κ(G) = n − m. The simplices with the vertex set V (G) and with the vertex set E(G) are denoted by ∆ V (G) and ∆ E(G) respectively. Notice that dim...

Ngày tải lên: 08/08/2014, 12:23

... appear off the blocks H jj and H kk . Case 3 : The three rows of L belong to three different zones, zones i, j,andk,with i, j,andk distinct. Select l distinct from i, j,andk. Consider the three ... Codes Crytogr.,toappear. [3] A. Blass and F. Harary, Properties of almost all graphs and complexes, J. Graph Theory 3 (1979), 225–240. [4] A. Blass, G. Exoo, and F. Harary, Paley graphs satis...

Ngày tải lên: 07/08/2014, 06:22

... J. Herzog, and T. Hibi. Shifting operations and graded Betti numbers. J. Algebraic Combin., 12:207–222, 2000. [3] D. Bayer, H. Charalambous, and S. Popescu. Extremal Betti numbers and applica- tions ... the number of (k − 1)-faces and the number of k-faces in a simplicial complex is given by Kruskal-Katona theorem [14, 12], and the relationship between the number of monomial...

Ngày tải lên: 07/08/2014, 08:22

... Fibonacci numbers. These distribu- tions will give us q-Fibonacci numbers which are related to the q-Fibonacci numbers of Carlitz [2], Cigler [3, 4], and Goyt and Sagan [6]. Let the n th Fibonacci number ... where F n = F n−1 + F n−2 and F 0 = 1 and F 1 = 1. Let [n] = {1, 2, . . . n} and [k, n] = {k, k + 1, . . . , n}. We will call two integer sequences a 1 a 2 . . . a k and b 1...

Ngày tải lên: 08/08/2014, 01:20

... Lemma 1 implies that y and z are the roots of graphs of A in G −{e 1 ,e 2 }.LetL and L  be the graph with root in y and z, respectively. By Lemma 14 and Lemma 15 we have that L and L  are isomorphic ... E(H)=E(L)∪E(L  ). Since κ(H +xy) ≥ 2, the subgraphs L and L  are not vertex -disjoint. Then H is obtained by sticking together L and L  . We stick together L and L  in su...

Ngày tải lên: 07/08/2014, 08:22

... separate v 1 and v 2 ). We can also assume that d(v 1 , v 2 ) ≤ r: otherwise, v 1 /∈ B r (v 2 ) and v 1 and v 2 are not twins. Consider the two paths between x and v 1 on the one hand, x and v 2 on ... that x ∈ B r (b) and x /∈ B r (a). Because a and b are adjacent, we have d(b, x) = r and d(a, x) = r + 1, which means that a and any vertices forming a shortest path between b...

Ngày tải lên: 07/08/2014, 15:22