具有乘适当断面无交并性质的富足半群

本文主要研究了具有乘适当断面无交并性质的富足半群的若干性质,并证明了半群为具有乘适当断面无交并性质的富足半群当且仅当它是一个矩形带和适当半群的直积。     

Hitting all maximum cliques with a stable set using lopsided independent transversals

Rabern recently proved that any graph with contains a stable set meeting all maximum cliques. We strengthen this result, proving that such a stable set exists for any graph with . This is tight, i.e. the inequality in the statement must be strict. The proof relies on finding an independent transversal in a graph partitioned into vertex sets of unequal size. © 2010 Wiley Periodicals, Inc. J Graph Theory 67:300‐305, 2011     

Line Transversals in Large <Emphasis Type="Italic">T</Emphasis>(3)- and <Emphasis Type="Italic">T</Emphasis>(4)-Families of Congruent Discs

A family of closed discs is said to have property T(k) if to every subset of at most k discs there belongs a common line transversal. A family of discs is said to be d-disjoint, d≥1, if the mutual distance between the centers of the discs is larger than d. It is known that a d-disjoint T(3)-family ℱ of unit diameter discs has a line transversal if . Similarly, a d-disjoint T(4)-family has a line transversal if . Both results are sharp in d, i.e., they do not hold for smaller values of d. The main result of this paper is that while the above lower bounds on d cannot be relaxed in general, some reduction of d can be compensated by imposing a proper d-dependent lower bound on the size of the family in both cases.     

具有Clifford断面的正则纯正半群

给出了具有Clifford断面的右正规纯正半群的等价刻画,得到了具有Clifford断面的正则纯正半群的次直积分解,证明了具有Clifford断面的正则纯正半群一定是正则纯正群．     

An improvement on H design

An H(m, g, 4, 3) is a triple , where X is a set of mg points, is a partition of X into m disjoint sets of size g, and is a set of 4‐element transverses of , such that each 3‐element transverse of is contained in exactly one of them. Such a design was introduced by Hanani 2 , who used it to study Steiner quadruple systems. Mills showed that for , an H(m, g, 4, 3) exists if and only if mg is even and is divisible by 3, and that for , an H(5, g, 4, 3) exists if g is divisible by 4 or 6 10 . In this article, we shall show that an H(5, g, 4, 3) exists if g is even, and . © 2008 Wiley Periodicals, Inc. J Combin Designs 17: 25–35, 2009     

关于极大前缀码的刻划的一个注记

设X*是字母表X上的自由幺半群,以X*为顶点集构造一个语言图Γ(X*),引入语言图Γ(X*)的横截集的概念,给出了前缀码为极大前缀码的一个刻划,并推广了相关文献的结果.     

On the remoteness function in median graphs

A profile on a graph G is any nonempty multiset whose elements are vertices from G. The corresponding remoteness function associates to each vertex x∈V(G) the sum of distances from x to the vertices in the profile. Starting from some nice and useful properties of the remoteness function in hypercubes, the remoteness function is studied in arbitrary median graphs with respect to their isometric embeddings in hypercubes. In particular, a relation between the vertices in a median graph G whose remoteness function is maximum (antimedian set of G) with the antimedian set of the host hypercube is found. While for odd profiles the antimedian set is an independent set that lies in the strict boundary of a median graph, there exist median graphs in which special even profiles yield a constant remoteness function. We characterize such median graphs in two ways: as the graphs whose periphery transversal number is 2, and as the graphs with the geodetic number equal to 2. Finally, we present an algorithm that, given a graph G on n vertices and m edges, decides in O(mlogn) time whether G is a median graph with geodetic number 2.     

Associate inverse subsemigroups of regular semigroups

By an associate inverse subsemigroup of a regular semigroup S we mean a subsemigroup T of S containing a least associate of each x∈S, in relation to the natural partial order ≤ _S . We describe the structure of a regular semigroup with an associate inverse subsemigroup, satisfying two natural conditions. As a particular application, we obtain the structure of regular semigroups with an associate subgroup with medial identity element. Research supported by the Portuguese Foundation for Science and Technology (FCT) through the research program POCTI.