Let G = × i=1 Cli be the direct product of cycles. It is proved that for any r ≥ 1, and any n ≥ 2, each connected component of G contains an r-perfect code provided that each li is a multiple of r n +(r+1). On the other hand, if a code of G contains a given vertex and its canonical local vertices, then any li is a multiple of r + (r + 1). It is also proved that an r-perfect code (r ≥ 2) of G is...

A variety of relationships between graph parameters involving packings, perfect neighbourhood, irredundant and R-annihilated sets is obtained. Some of the inequalities are improvements of existing bounds for the lower irredundance number, and others are motivated by the conjecture (recently disproved) that for any graph the smallest cardinality of a perfect neighbourhood set is at most the lowe...

let $r$ be a right artinian ring or a perfect commutative‎‎ring‎. ‎let $m$ be a noncosingular self-generator $sum$-lifting‎‎module‎. ‎then $m$ has a direct decomposition $m=oplus_{iin i} m_i$‎,‎where each $m_i$ is noetherian quasi-projective and each‎‎endomorphism ring $end(m_i)$ is local‎.

Let R be a commutative ring. An R-module M is called co-multiplication provided that foreach submodule N of M there exists an ideal I of R such that N = (0 : I). In this paper weshow that co-multiplication modules are a generalization of strongly duo modules. Uniserialmodules of finite length and hence valuation Artinian rings are some distinguished classes ofco-multiplication rings. In additio...

For spherically symmetric relativistic perfect fluid models, the well-known Buchdahl inequality provides the bound 2M/R 6 8/9, where R denotes the surface radius and M the total mass of a solution. By assuming that the ratio p/ρ be bounded, where p is the pressure, ρ the density of solutions, we prove a sharper inequality of the same type, which depends on the actual bound imposed on p/ρ. As a ...

We consider the (r, l)-Partization problem of finding a set of at most k vertices whose deletion results in a graph that can be partitioned into r independent sets and l cliques. Restricted to perfect graphs and split graphs, we describe sequacious fixed-parameter tractability results for (r, 0)-Partization, parameterized by k and r. For (r, l)-Partization where r + l = 2, we describe an O∗(2k)...

Let $R$ be a right artinian ring or a perfect commutative‎‎ring‎. ‎Let $M$ be a noncosingular self-generator $sum$-lifting‎‎module‎. ‎Then $M$ has a direct decomposition $M=oplus_{iin I} M_i$‎,‎where each $M_i$ is noetherian quasi-projective and each‎‎endomorphism ring $End(M_i)$ is local‎.

The copyright law of the United States (title 17, U.S. Code) governs the making of photocopies or other reproductions of copyrighted material. Any copying of this document without permission of its author may be prohibited by law. Perfect matchings in random i—regular, 5—uniform hypergraphs.

A latin transversal in a square matrix of order n is a set of entries, no two in the same row or column, which are pairwise distinct. A longstanding conjecture of Ryser states that every Latin square with odd order has a latin transversal. Some results on the existence of a large partial latin transversal can be found in [11,6,16]. Mainly motivated by Ryser’s conjecture, Erdős and Spencer [8] p...

What largeness and structural assumptions on A ⊆ [R]ω can guarantee the existence of a non-empty perfect set P ⊆ R such that [P ]ω ⊆ A? Such a set P is called A-homogeneous. We show that even if A is open, in general it is independent of ZFC whether for a cardinal κ, the existence of an A-homogeneous set H ∈ [R]κ implies the existence of a non-empty perfect A-homogeneous set. On the other hand,...