Ramsey数R(K_3,K_(16)-e)的一个下界

图论方法是研究Ramsey理论中最常用的方法,80多年的研究产生了大量的成果.Ramsey数R(G,H)是这样的最小正整数n,使得完全图K_n的边的任何一种红、蓝染色都会有一个红色边子图G,或者有一个蓝色边子图H.本文找到Ramsey数R(K_3,K_(16-e))的一个下界.     

素数阶循环图和经典Ramsey数R（4，n）的三个新下界

研究了素数阶循环圈的基本性质，提出了寻求有效参数构造正则循环圈的新方法，得到了3个经典Ramsey数的新下界：R（4，17）≥164，R（4，18）≥182，R（4，22）≥282．这前2个结果填补了关于Ramsey数综述[2]的上下界表中的2个空白，第3个结果超过了目前已知的最好下界R（4，22）≥258，     

树的Hk-cordial性

如果可以给图G的边用集合（±1,±2,.. ,±k）中的元素标号,使得对G每个顶点u,其标号,即所有与其相邻的边的标号之和,都落在集合（±1,±2,.. ,±k）中,且Ie（i）-e（-i）I≤1和lu（i）-u（-i）1≤1,其中t心）和e（i）（1≤i≤k）分别是标号为i的顶点数和边数,那么就称该图G为Hk-cordial的．本文证明了除了尥以外,每棵树都是H3-cordial的．     

On the Edge-forwarding Indices of Frobenius Graphs

A G-Frobenius graph F, as defined by Fang, Li, and Praeger, is a connected orbital graph of a Frobenius group G = K × H with Frobenius kernel K and Frobenius complement H. F is also shown to be a Cayley graph, F = Cay（K, S） for K and some subset S of the group K. On the other hand, a network N with a routing function R, written as （N, R）, is an undirected graph N together with a routing R which consists of a collection of simple paths connecting every pair of vertices in the graph. The edge-forwarding index π（N） of a network （N, R）, defined by Heydemann, Meyer, and Sotteau, is a parameter to describe tile maximum load of edges of N. In this paper, we study the edge-forwarding indices of Frobenius graphs. In particular, we obtain the edge-forwarding index of a G-Frobenius graph F with rank（G） ≤ 50.     

交换环上矩阵代数的局部化导子

Let R be a commutative ring with identity, Nn（R） the matrix algebra consisting of all n × n strictly upper triangular matrices over R. Several types of proper local derivations of Nn（R） （n ≤ 4） are constructed, based on which all local derivations of Nn（R） （n ≤ 4） are characterized when R is a domain.     

含有溶质的流体在两层多孔介质中的渗流问题

本文讨论含有溶质的流体在两层多孔介质中的渗流问题，即（θ（x，U）t=（K（x，U）Ux-K（x，U））x，（x，t）∈GT，（θ（x，U）V（x，t）t=（DθVx）x-（V（KUx-K））x，（x，t）∈GT，U（x，0）=U0（x），V（x，0）=V0（x），0≤x≤2，U（0，t）-h0（t），U（2，t）=h2（t），0≤t≤T，V（0，t）=g0（t），V（2，t）=g2（t），0≤t≤T。其中θ（x,U)=θ1(x,U)，当（x,t)∈D1=｛0≤x≤1,0≤t≤T｝；θ（x,U)=θ2(x,U)当（x,t）∈D2＋1｛1＜x≤2，0≤t≤T｝。K（x,U)=K1(x,U)当（x,t)∈D1;K(x,U)=K2(x,U)，当(x,t)∈D2。θi，Ki分别是Di上的介质含水率及水力传导率，V是溶质的浓度，此外还要求U，V，K（x,U)(Ux-1)及DθVx V(KUx-K)在x=1连续。     

9个经典Ramsey数R(3,t)的新下界

本文研究了经典Ramsey数R(3,t)的下界问题.利用素数阶循环图的性质改进一般阶循环图团数的计算方法,获得了9个经典Ramsey数R(3,t)的新下界:R(3,29)≥183,R(3,30)≥189,R(3,32)≥213,R(3,33)≥218,R(3,34)≥226,R(3,35)≥231,R(3,36)≥239,R(3,37)≥244,R(3,38)≥256,其中前三个结果分别改进了迄今已知的最好的下界,后6个结果是本文首次报道的.     

L_p-John椭球的极值性质

对于0n中的凸体K,Lutwak,Yang和Zhang定义了L_p-John椭球E_pK的概念.本文证明了下面两个结论:（i）对Rⁿ中任意原点中心对称凸体K,存在一个椭球E和一个超平行体P,使得当1≤p≤∞和0-1ω_n¹/nE■EpK■2ω_n^-1/nn^1/q-1/2EqP,且V（E）=V（K）=V（P）;当1≤p≤∞和2≤q≤∞时,有n^1/q-1/2EqP■EpK■E,且V（E）=V（K）=V（P）.（ii）设K是Rⁿ中John点在原点的凸体,则存在一个单形T,使得当1≤p≤∞和0pK■α_nn^1/q-1/2EqT,且V（K）=V（T）;当1≤p≤∞和2nKn^1/q-1/2EqT且V（K）=V（T）.     

Gini平均值公开问题的解

对固定的（a,b）∈R×R,Gini平均值S（a,b;x,y）关于（x,y）∈（0,∞）×（0,∞）的Schur凸性或Schur凹性问题是目前的一个公开问题.本文证明了S（a,b;x,y）关于（x,y）∈（0,∞）×（0,∞）为Schur凸当且仅当（a,b）∈{（a,b）：a≤0,b≤0,a＋b1}以及Schur凹当且仅当（a,b）∈{（a,b）：b≤0,b≤a,a＋b≤1}∪{（a,b）：a≤0,a≤b,a＋b≤1}.     

不等式背景下的函数求值问题

众所周知,不等式a≤c≤a中蕴涵着等量关系c=a,不等式g（x）≤f（x＋k）-f（x）≤g（x）（x∈R）中蕴涵着等量关系f（x＋k）-f（x）-g（x）．若函数g（x）已知,再给出f（x0）的值以及n（n∈R且n≥2）,就可以求出f（x0＋nk）=f（x0）＋∑i=0^n-1g（x0＋ik）这一函数值．     

代数构造及在Ramsey理论中的应用

本文在Galois域上的代数构造和关于一些特定类型图的Ramseyr数之间建立了一个关系．关键问题是研究了关于Galois域上的代数构造的方程及方程组的解．我们得到了一些关于二部图的新的下界和上界．     

代数构造及在Ramsey理论中的应用

这篇文章在伽罗瓦域上的代数构造和关于一些特定类型图的Ramsey数之间建立了一个关系. 研究了关于伽罗瓦域上的代数构造的方程及方程组的解. 我们得到了一些关于二部图的Ramsey数的新的下界和上界.     

Canonical Pattern Ramsey Numbers

A color pattern is a graph whose edges have been partitioned into color classes. A family of color patterns is a Ramsey family provided there is some sufficiently large integer N such that in any edge coloring of the complete graph K_N there is an (isomorphic) copy of at least one of the patterns from . The smallest such N is the Ramsey number of the family . The classical Canonical Ramsey theorem of Erds and Rado asserts that the family of color patterns is a Ramsey family if it consists of monochromatic, rainbow (totally multicolored) and lexically colored complete graphs. In this paper we treat the asymmetric case by studying the Ramsey number of families containing a rainbow triangle, a lexically colored complete graph and a fixed arbitrary monochromatic graph. In particular we give asymptotically tight bounds for the Ramsey number of a family consisting of rainbow and monochromatic triangle and a lexically colored K_N. Among others, we prove some canonical Ramsey results for cycles.     

对于K2+Tm和完全图的Ramsey函数的渐近上界

本文研究了当n趋于无穷大时,关于K2+Tm和完全图Kn的Ramsey数的渐近上界,以及r(K2+Tm,Kn)和r(K1+Tm,Kn)的渐近关系.利用李雨生等人所给出的一个独立数的下界公式,给出了r(K4,Kn)和r(Kk-c,Kn)的渐近上下界,推广了李雨生等人所给出的r(K1+Tm,Kn)的下界.     

Conditions on Ramsey Nonequivalence

Given a graph H , a graph G is called a Ramsey graph of H if there is a monochromatic copy of H in every coloring of the edges of G with two colors. Two graphs G , H are called Ramsey equivalent if they have the same set of Ramsey graphs. Fox et al. (J Combin Theory Ser B 109 (2014), 120–133) asked whether there are two nonisomorphic connected graphs that are Ramsey equivalent. They proved that a clique is not Ramsey equivalent to any other connected graph. Results of Ne?et?il et al. showed that any two graphs with different clique number (Combinatorica 1(2) (1981), 199–202) or different odd girth (Comment Math Univ Carolin 20(3) (1979), 565–582) are not Ramsey equivalent. These are the only structural graph parameters we know that “distinguish” two graphs in the above sense. This article provides further supportive evidence for a negative answer to the question of Fox et al. by claiming that for wide classes of graphs, the chromatic number is a distinguishing parameter. In addition, it is shown here that all stars and paths and all connected graphs on at most five vertices are not Ramsey equivalent to any other connected graph. Moreover, two connected graphs are not Ramsey equivalent if they belong to a special class of trees or to classes of graphs with clique‐reduction properties.     

Improved Upper Bounds for Gallai–Ramsey Numbers of Paths and Cycles

Given a graph G and a positive integer k, define the Gallai–Ramsey number to be the minimum number of vertices n such that any k‐edge coloring of contains either a rainbow (all different colored) triangle or a monochromatic copy of G. In this work, we improve upon known upper bounds on the Gallai–Ramsey numbers for paths and cycles. All these upper bounds now have the best possible order of magnitude as functions of k.     

用Paley图计算对角Ramsey数下界的新方法

本文研究了对角Paley数的下界问题.利用一个新发现的Paley图的自同构,给出了计算Paley图团数的一个新方法,获得了2个对角Rasey数的新下界:R(20,20)≥18877,R(21,21)≥25949.     

Some geometric structures and bounds for Ramsey numbers

We investigate several bounds for both K_2,m−K_1,n Ramsey numbers and K_2,m−K_1,n bipartite Ramsey numbers, extending some previous results. Constructions based on certain geometric structures (designs, projective planes, unitals) yield classes of near-optimal bounds or even exact values. Moreover, relationships between these numbers are also discussed.