One-Element Extensions in the Variety Generated by Tournaments

We investigate congruences in one-element extensions of algebras in the variety generated by tournaments.     

赋权矩阵及其性质

本文给出了以S为行权和向量的权矩阵类T_＋(S)中每个权矩阵都可逆的一个充要条件．     

LA RECONSTRUCTION DES TOURNOIS SANS DIAMANT

We prove that if T is a tournament of order n > 6 in which any 4-sub-tournament is hamiltonian or transitive, then T is reconstructible in the sense of Ulam.     

Structure theorem for tournaments omitting N5

A finite tournament T is tight if the class of finite tournaments omitting T is well‐quasi‐ordered. We show here that a certain tournament N₅ on five vertices is tight. This is one of the main steps in an exact classification of the tight tournaments, as explained in [10]; the third and final step is carried out in [11]. The proof involves an encoding of the indecomposable tournaments omitting N₅ by a finite alphabet, followed by an application of Kruskal's Tree Theorem. This problem arises in model theory and in computational complexity in a more general form, which remains open: the problem is to give an effective criterion for a finite set {T₁,…,T_k} of finite tournaments to be tight in the sense that the class of all finite tournaments omitting each of T₁,…,T_k is well‐quasi‐ordered. © 2003 Wiley Periodicals, Inc. J Graph Theory 42: 165–192, 2003     

福建省首届大学生化学实验邀请赛无机及分析化学实验试题解析

介绍了福建省首届大学生化学实验邀请赛无机及分析化学实验的命题思路、试题原题及评分规则,并对实验中存在的问题及成绩进行了总结分析。     

A lower bound on the size of an absorbing set in an arc-coloured tournament

Bousquet, Lochet and Thomassé recently gave an elegant proof that for any integer $n$, there is a least integer $f\left(n\right)$ such that any tournament whose arcs are coloured with $n$ colours contains a subset of vertices $S$ of size $f\left(n\right)$ with the property that any vertex not in $S$ admits a monochromatic path to some vertex of $S$. In this note we provide a lower bound on the value $f\left(n\right)$.     

Uniform frames with block size four and index one or three

Abstact: In this article, we present a new construction to obtain uniform frames with block size four and index one. The known existence results for (4, 1)‐frames and (4, 3)‐frames are both improved with a small number of possible exceptions. © 2000 John Wiley & Sons, Inc. J Combin Designs 9: 28–39, 2001     

扩充竞赛图的(1,2)步竞争图

2011年Factor等人提出了有向图的(1,2)步竞争图的概念,并完全刻画了竞赛图的(1,2)步竞争图.设D=(V,A)是一个有向图.如果无向图G=(V,E)满足,V(G)=V(D)并且xy∈E(G)当且仅当D中存在顶点z≠x,y使得d_(D-y)(x,z)=1,d_(D-x)(y,z)≤2或者d_(D-x)(y,z)=1,d_(D-y)(x,z)≤2,那么称G为D的(1,2)步竞争图,记为C_(1,2)(D).本文主要刻画了扩充竞赛图的(1,2)步竞争图.     

Monochromatic sinks in nearly transitive arc-colored tournaments

Let T be the set of all arc-colored tournaments, with any number of colors, that contain no rainbow 3-cycles, i.e., no 3-cycles whose three arcs are colored with three distinct colors. We prove that if T∈T and if each strong component of T is a single vertex or isomorphic to an upset tournament, then T contains a monochromatic sink. We also prove that if T∈T and T contains a vertex x such that T−x is transitive, then T contains a monochromatic sink. The latter result is best possible in the sense that, for each n≥5, there exists an n-tournament T such that (T−x)−y is transitive for some two distinct vertices x and y in T, and T can be arc-colored with five colors such that T∈T, but T contains no monochromatic sink.     

Remarks on the second neighborhood problem

The second neighborhood conjecture of Seymour asserts that for any orientation G = (V,E), there exists a vertex υ ∈ V so that |N⁺(υ)| ≤ |N⁺⁺(υ)|. The conjecture was resolved by Fisher for tournaments. In this article, we prove the second neighborhood conjecture for several additional classes of dense orientations. We also prove some approximation results, and reduce an asymptotic version of the conjecture to a finite case. © 2007 Wiley Periodicals, Inc. J Graph Theory 55: 208–220, 2007