Upper bounds on the signed (k, k)-domatic number

Let G be a graph with vertex set V(G), and let f : V(G) → {?1, 1} be a two-valued function. If k ≥ 1 is an integer and ${\sum_{x\in N[v]} f(x) \ge k}$ for each ${v \in V(G)}$ , where N[v] is the closed neighborhood of v, then f is a signed k-dominating function on G. A set {f ₁,f ₂, . . . ,f _d } of distinct signed k-dominating functions on G with the property that ${\sum_{i=1}^d f_i(x) \le k}$ for each ${x \in V(G)}$ , is called a signed (k, k)-dominating family (of functions) on G. The maximum number of functions in a signed (k, k)-dominating family on G is the signed (k, k)-domatic number of G. In this article we mainly present upper bounds on the signed (k, k)-domatic number, in particular for regular graphs.     

New upper bounds on the minimum size of covering designs

Let D = {B₁, B₂,…, B_b} be a finite family of k-subsets (called blocks ) of a v-set X(v) = {1, 2,…, v} (with elements called points ). Then D is a (v, k, t) covering design or covering if every t-subset of X(v) is contained in at least one block of D. The number of blocks, b, is the size of the covering, and the minimum size of the covering is called the covering number , denoted C(v, k, t). This article is concerned with new constructions of coverings. The constructions improve many upper bounds on the covering number C(v, k, t) © 1998 John Wiley & Sons, Inc. J Combin Designs 6:21–41, 1998     

Upper bounds on the independence and the clique covering number

New upper bounds for the independence number and for the clique covering number of a graph are given in terms of the rank, respectively the eigenvalues, of the adjacency matrix. We formulate a conjecture concerning an upper bound of the clique covering number. This upper bound is related to an old conjecture of Alan J. Hoffman which is shown to be false. Key words: adjacency matrix, eigenvalues, independence number, clique covering number. AMS classification: 05C.     

Upper bounds on the upper signed total domination number of graphs

Let G=(V,E) be a graph. A function f:V→{−1,+1} defined on the vertices of G is a signed total dominating function if the sum of its function values over any open neighborhood is at least one. A signed total dominating function f is minimal if there does not exist a signed total dominating function g, f≠g, for which g(v)≤f(v) for every v∈V. The weight of a signed total dominating function is the sum of its function values over all vertices of G. The upper signed total domination number of G is the maximum weight of a minimal signed total dominating function on G. In this paper we present a sharp upper bound on the upper signed total domination number of an arbitrary graph. This result generalizes previous results for regular graphs and nearly regular graphs.     

Embeddings of Sλ(2, 4, v)

It is shown that the necessary condition for a given S_λ(2,4,u) to be embedded in some S_λ(2,4,v) as a subdesign, namely v ≥ 3u + 1, is also sufficient for the case of λ = 6. Combining this with the previously known results gives the same sufficiency for any positive integer λ. © 1994 John Wiley & Sons, Inc.     

3-齐次群与旗传递5-（v，k，3）设计

旗传递t-设计的分类是代数组合学的一个重要课题．本文主要讨论了旗传递5-（v,k,3）设计．由P．J．Cameron和C．E．Praeger的结论可知,此时设计的自同构群是3-齐次群．本文利用3-齐次群的分类,证明了设计的自同构群不能是仿射型群．     

Upper Bounds on the Dual Distance of BCH(255, k)

To obtain upper bounds on the distance of a binary linear code, many probabilistic algorithms have been proposed. The author presents a general variation to these algorithms, specific for cyclic codes, which is shown to be an improvement. As an example, the author optimizes Brouwer's algorithm to find the best upper bounds on the dual distance of BCH[255,k,d].     

On the Spectrum of Steiner (v,k,t) Trades (II)

 A (v,k,t) trade T=T ₁−T ₂ of volume m consists of two disjoint collections T ₁ and T ₂ each containing m blocks (k-subsets) such that each t-subset is contained in the same number of blocks in T ₁ and T ₂. If each t-subset occurs at most once in T ₁, then T is called a Steiner (k,t) trade. In this paper, we continue our investigation of the spectrum S(k,2); that is, the set of allowable volumes of Steiner (k,t) trades when t=2. By using the concept of linked trades, we show that 2k+1∈S(k,2) precisely when k∈{3, 4, 7}. Received: February 28, 1997     

Flag-transitive 2- $$(v,k,lambda )$$ ( v,k , λ ) designs with $$r>lambda (k-3)$$ r > λ ( k - 3 )

Designs, Codes and Cryptography - In this paper, we study the flag-transitive automorphism groups of 2-designs and prove that if G is a flag-transitive automorphism group of a 2-design $$mathcal...     

树的3-彩虹控制数的上界

对树的3-彩虹控制数进行研究,首先用构造法找到直径较小的树的3-彩虹控制数的上界.再通过分类讨论思想和数学归纳法得到一般的阶n大于等于5的树的3-彩虹控制数的上界.     

2-(v,k,1)设计和PSL(3,q)(q是奇数)

§ 1　 IntroductionA2 -(v,k,1 ) design D=(S,B) consists ofa finite set Sof v points and a collection Bof some subsets of S,called blocks,such that any two points lie on exactly one blockand each block contains exactly k points.A flag of Dis a pair(α,B) such thatα∈S,B∈Bandα∈B,the set of all flags is denoted by F.We assume that2≤k≤v.An automorphism of Dis a permutation of the points which leaves the set Binvari-ant,all the automorphisms form a group Aut D.Let G be a subgroup of A…     

New star discrepancy bounds for (t,m,s)-nets and (t,s)-sequences

In this paper, we derive new general upper bounds on the star discrepancy of $(t,m,s)$ -nets and $(t,s)$ -sequences. These kinds of point sets are among the most widely used in quasi-Monte Carlo methods for numerical integration. By our new results, we improve on previous discrepancy bounds and prove a conjecture stated by the second author in an earlier paper.     

Steinberg triality groups acting on 2 - (v, k, 1) designs

A 2 - (v,k,1) design D = (P, B) is a system consisting of a finite set P of v points and a collection B of k-subsets of P, called blocks, such that each 2-subset of P is contained in precisely one block. Let G be an automorphism group of a 2- (v,k,1) design. Delandtsheer proved that if G is block-primitive and D is not a projective plane, then G is almost simple, that is, T ≤ G ≤ Aut(T), where T is a non-abelian simple group. In this paper, we prove that T is not isomorphic to 3D4(q). This paper is part of a project to classify groups and designs where the group acts primitively on the blocks of the design.     

Virtually balanced incomplete block designs for v = 22, k = 8, and λ = 4

When basic necessary conditions for the existence of a balanced incomplete block design are satisfied, the design may still not exist or it may not be known whether it exists. In either case, other designs may be considered for the same parameters. In this article we introduce a class of alternative designs, which we will call virtually balanced incomplete block designs. From a statistical point of view these designs provide efficient alternatives to balanced incomplete block designs, and from a combinatorial point of view they offer challenging new questions. © 1995 John Wiley & Sons, Inc.     

On the existence of pure (v, 4, λ)-PMD with λ = 1 and 2

In this article, we investigate the existence of pure (v, 4, λ)-PMD with λ = 1 and 2, and obtain the following results: (1) a pure (v, 4, 1)-PMD exists for every positive integer v = 0 or 1 (mod 4) with the exception of v = 4 and 8 and the possible exception of v = 12; (2) a pure (v, 4, 2)-PMD exists for every integer v ≥ 6. © 1994 John Wiley & Sons, Inc.     

Suzuki群Sz(q)与2-(v,k,1)区组设计

§ 1　IntroductionA2 -( v,k,1 ) design D=( Ω,B) is a system consisting of a finite setΩ ofv points anda collection Bofk-subsets ofΩ ,called blocks,such thatany 2 -subsetofΩ is contained inexactly one block.We shall always assume that2 相似文献   

Flag-Transitive 3-(v,k, 3) Designs and PSL(2, q) Groups

This article is a contribution to the study of the automorphism groups of 3-(v,k,3) designs.Let S =(P,B) be a non-trivial 3-(q+ 1,k,3) design.If a two-dimensional projective linear group PSL(2,q) acts flag-transitively on S,then S is a 3-(q + 1,4,3) or 3-(q + 1,5,3) design.     

All v(3, t)'s exist for 3t + 1 a prime

The existence of a V(3,t), for any prime 3t+1 is proved constructively. A V(m,t) is equivalent to m idempotent pairwise orthogonal Latin squares of order (m+1)t + 1 with one hole of order t. © 1995 John Wiley & Sons, Inc.