带两洞的不完全自正交拉丁方的存在性

讨论不完全自正交拉丁方ISOLS(v;3,3)的存在性问题.证明当v≥12,v{13,14,15,16,17,18,19,20,21,22,23,24,25,27,28,29,30,31,33,35,36}时,存在ISOLS(v;3,3).     

弦图的L(3,2,1)}-标号

图 G 的一个 L(3,2,1)- 标号是指从 V(G) 到非负整数集的一个映射 f, 满足: 当 d_G(u,v)=1 时, |f(u)-f(v)|\geq 3; 当 d_G(u,v)=2 时, |f(u)-f(v)|\geq 2; 当 d_G(u,v)=1 时, |f(u)-f(v)|\geq 1. L(3,2,1)-标号问题就是确定出最小的整数 \lambda_3(G) 使得 G存在最大标号不超过该数的 L(3,2,1)- 标号. 本文研究了弦图的 L(3,2,1)- 标号问题,获得了弦图及其一些子类, 如扇, r- 路,r- 树等的 \lambda_3 数的界.     

Decompositions of the 3-uniform hypergraphs K(3)v into hypergraphs of a certain type

In this paper, we investigate a generalization of graph decomposition, called hypergraph decomposition. We show that a decomposition of a 3-uniform hypergraph K(3)v into a special kind of hypergraph K(3)4 - e exists if and only if v ≡ 0, 1, 2 (mod 9) and v ≥ 9.     

半无爪可迹图的度和条件

可迹图即为一个含有Hamilton路的图.令$N[v]=N(v)\cup\{v\}$, $J(u,v)=\{w\in N(u)\cap N(v):N(w)\subseteq N[u]\cup N[v]\}$.若图中任意距离为2的两点$u,v$满足$J(u,v)\neq \emptyset$,则称该图为半无爪图.令$\sigma_{k}(G)=\min\{\sum_{v\in S}d(v):S$为$G$中含有$k$个点的独立集\},其中$d(v)$表示图$G$中顶点$v$的度.本论文证明了若图$G$为一个阶数为$n$的连通半无爪图,且$\sigma_{3}(G)\geq {n-2}$,则图$G$为可迹图; 文中给出一个图例,说明上述结果中的界是下确界; 此外,我们证明了若图$G$为一个阶数为$n$的连通半无爪图,且$\sigma_{2}(G)\geq \frac{2({n-2})}{3}$,则该图为可迹图.     

图2Kv的可旋转(4,6)圈系

证明了图2Kv的可旋转（4，6）圈系存在的充分必要条件为：v≥10，v≡0，5（mod 10）．     

树的L(3,2,1)-标号问题

An L(3,2,1)-labeling of a graph G is a function f from the vertex set V(G) to the set of all non-negative integers(labels) such that |f(u)-f(v)|≥3 if d(u,v)=1,|f(u)-f(v)≥2 if d(u,v)=2 and |f(u)-f(v)|≥1 if d(u,v)=3.For a non-negative integer k,a k-L(3,2,1)-labeling is an L(3,2,1)-labeling such that no label is greater than k.The L(3,2,1)-labeling number of G,denoted by λ_(3,2,1)(G), is the smallest number k such that G has a k-L(3,2,1)-labeling.In this article,we characterize the L(3,2,1)-labeling numbers of trees with diameter at most 6.     

λ-重K_(1,4)-设计到λ-重K_(1,3)-最大填充的变形

令(X,B)为一个u阶的λ-重K_(1,4)-设计.对于每一个区组B=(a:b,c,d,e)∈B,若删去边{a,e},则得到一个K_(1,3)[a:b,c,d].令C为删去B中每一个区组的边{a,e}而得到的K_(1,4)的集合,F为被删去的边构成的集合.若F可以被重组成[λv(v-1)/24]个K_(1,3)的集合D,则(X,CUD)为一个v阶λ-重K_(1,3)-最大填充.称(X,C∪D)为λ-重K_(1,4-)设计(X,B)的变形.本文证明了v阶λ-重K_(1,4)-设计到u阶λ-重K_(1,3)-最大填充的变形存在的充要条件是λv(v-1)≡0(mod 8)且v≥5.     

The $L(3, 2, 1)$-Labeling on Bipartite Graphs

An $L(3, 2, 1)$-labeling of a graph $G$ is a function from the vertex set $V(G)$ to the set of all nonnegative integers such that $|f(u)−f(v)|≥3$ if $d_G(u, v)=1$, $|f(u)−f(v)|≥2$ if $d_G(u, v)=2$, and $|f(u)−f(v)|≥1$ if $d_G(u, v)=3$. The $L(3, 2, 1)$-labeling problem is to find the smallest number $λ_3(G)$ such that there exists an $L(3, 2, 1)$-labeling function with no label greater than it. This paper studies the problem for bipartite graphs. We obtain some bounds of $λ_3$ for bipartite graphs and its subclasses. Moreover, we provide a best possible condition for a tree $T$ such that $λ_3(T)$ attains the minimum value.     

两类图的L(2.1)-标号数

图G的一个L(2.1)-标号是从顶点集V(G)到非负整数的一个函数f,使得若d(u,v)=1时,有|f(u)-f(v)|≥2;若d(u,v)=2时,有|f(u)-f(v)|≥1.图G的L(2.1)-标号数λ(G)是G的所有L(2.1)-标号下的跨度max{f(v):v∈V(G)}的最小数.图Fn+1*为扇图的路上每个顶点增加一个悬挂边得到的图.图Hn为轮图的圈上每个顶点增加一个悬挂边得到的图.本文确定了图Fn+1*与Hn的L(2.1)-标号数.     

一类含有奇数个顶点的三色有向图本原指数上界

一个三色有向图D是本原的,当且仅当存在非负整数h、k和v,且h+k+v0,使得D中的每一对顶点(i,j)都存在从i到j的(h,k,v)-途径,h+k+v的最小值定义为三色有向图D的本原指数.研究了一类三色有向图,它的未着色图中包含2佗-4个顶点,一个n-圈、一个(n-2)-圈和一个2-圈,给出了本原指数上界.     

关于P_(r,(2s-1))的奇优美标号

对于简单图G=〈V,E〉,如果存在一个映射f:V(G)→{0,1,2,…,2 |E|-1}满足1)对任意的u,v∈V,若u≠v,则(u)≠f(v);2)max{f(v)|v∈V}=2|E|-1;3)对任意的e_1,e_2∈E,若e_1≠e_2,则g(e_1)≠g(e_2),此处g(e)=|f(u)+f(v)|,e=uv;4){g(e)|e∈E}={1,3,5,…,2|E|-1},则称G是奇优美图,f称为G的奇优美标号.Gnanajoethi提出了一个猜想:每棵树都是奇优美的.证明了图P_(r,(2s-1)是奇优美图.     

本刊英文版Vol.29(2013),No.8论文摘要(英文)

<正>L(j,k)-number of Direct Product of Path and Cycle Wai Chee SHIU Qiong WU Abstract For positive numbers j and k,an L(j,k)-labeling f of G is an assignment of numbers to vertices of G such that |f(u)-f(v)|≥j if uv∈E(G),and |f(u)-f(v)|≥k if d(u,v)=2.Then the span of f is the difference between the maximum and the minimum numbers assigned by f.The L(j,k)-number of G,denoted byλ_(j,k)(G),is the minimum span over     

一个带非线性边界条件的强耦合抛物方程组的整体存在性与爆破

本文处理带非线性边界条件 u n=uα, v n=vβ ,(x ,t) ∈ Ω× (0 ,T)的抛物方程组ut =vpΔu ,vt=uqΔv ,(x ,t) ∈Ω× (0 ,T) ,其中Ω RN 为一个有界区域 ,p ,q>0和α ,β≥ 0为常数 .研究了上述问题正解的整体存在性和爆破 ,建立了整体存在和爆破的新标准 .证明了当max{p+β,q+α}≤ 1时正解 (u ,v)整体存在 ,当min{p+β ,q+α}>1且max{α ,β}<1时正解 (u ,v)在有限时刻爆破     

Automorphism subgroups for designs with $$\lambda =1$$ λ = 1

Designs, Codes and Cryptography - Given an integer $$k\ge 3$$ and a group G of odd order,&nbsp; if there exists a 2-(v,&nbsp;k,&nbsp;1)-design and if v is sufficiently large then there...     

具有给定指数的本原有向图的Hamilton性质

本文解决了１９８２年Ｊ．Ａ．Ｒｏｓｓ提出的两个问题,并得到如下结果：（１）设Ｄ是具有围长ｓ＞１和指数γ（Ｄ）＝ｎ＋ｓ（ｎ－２）的ｎ阶本原有向图,则Ｄ是Ｈａｍｉｌｔｏｎ的;（２）设Ｄ是含有环的ｎ阶本原有向图且γ（Ｄ）＝２ｎ－２,则Ｄ是Ｈａｍｉｌｔｏｎ的当且仅当ｍａｘ｛ｄ（ｕ,ｖ）|γ（ｕ,ｖ）＝２ｎ－２｝＝ｎ－２．     

Golf设计存在的谱

两个ｖ阶对称幂等拉丁方称为互不相交的若除对角线外，其余每一位置上的两个元互不相同．ｖ－２个互不相交的ｖ阶对称幂等拉丁方称为ｖ阶ｇｏｌｆ设计．本文证明了对任意大于１的奇数ｖ（ｖ≠５），除去２８个可能的例外值，均存在ｖ阶ｇｏｌｆ设计．     

A method of constructing generalized difference sets

On the elements of the ring of residues modulo v (zτ v, 3τ v) we construct cyclic PBIB-designs with τ(v)-1 classes of connectedness, where τ(v) is the number of divisors of v. We prove the existence of cyclic BIB-designs with parameters b, v, r, k, and λ such that: 1) λ=k (and also λ=k/2 if k is even), k≥4, and (k-1) ¦ (p-1) for each prime divisor p of the number v; 2) λ=(k?l)/2, k odd, k≥3, k ¦ (p?1) for each prime divisor p of the number v.     

直径为4的树的奇强协调性

对简单图G=〈V,E〉,如果存在一个映射f:V→{0,1,2,…,2 E-1}满足1)对任意的u,v∈V,若u≠v,则f(u)≠f(v);2)对任意的e1,e2∈E,若e1≠e2,则g(e1)≠g(e2),此处g(e)=f(u)+f(v),e=uv;3){g(e)e∈E}={1,3,5,…,2 E-1},则称G为奇强协调图,f称为G的奇强协调标号.给出了直径为4的树的奇强协调标号.     

若干图的点强全着色

图G(V,E)的一正常k-全着色σ称为G(V,E)的一个k-点强全着色,当且仅当v∈V(G),N[v]中的元素着不同颜色,其中N[v]={u|vu∈E(G)}∪{v}.并且vχsT(G)=min{k|存在G的一个k-点强全着色}称为G(V,E)的点强全色数.本文得到了一些特殊图的点强全色数χvTs(G),并提出猜想:对于简单图G,有k(G)≤χvTs(G)≤k(G)+1,这里k(G)表示图G中所有顶点间距离不超过2的点集的最大顶点数.     

Heavy cycles in 2-connected triangle-free weighted graphs

A weighted graph is one in which every edge e is assigned a nonnegative number, called the weight of e. The sum of the weights of the edges incident with a vertex v is called the weighted degree of v, denoted by dw(v). The weight of a cycle is defined as the sum of the weights of its edges. Fujisawa proved that if G is a 2-connected triangle-free weighted graph such that the minimum weighted degree of G is at least d, then G contains a cycle of weight at least 2d. In this paper, we proved that if G is a2-connected triangle-free weighted graph of even size such that dw(u) + dw(v) ≥ 2d holds for any pair of nonadjacent vertices u, v ∈ V(G), then G contains a cycle of weight at least 2d.