4一致反超图的最小边数问题

混合超图是在超图的基础上添加一个反超边得到的图．超边和反超边的区别主要体现在着色要求上．在着色中,要求每一超边至少要有两个点着不同的颜色,而每一反超边至少有两个点着相同的颜色．最大最小颜色数分别称为混合超图的上色数和下色数。本文主要研究反超图,即只含反超边的超图。讨论了上色数为3的4一致超图的最小边数问题．给出了上色数为3的4一致反超图的最小边数的一个上界和一个下界．     

Partitioning series-parallel multigraphs into ν *-excluding edge covers

We prove that, for any given vertex ν* in a series-parallel graph G, its edge set can be partitioned into κ = min{κ′(G) + 1, δ(G)} subsets such that each subset covers all the vertices of G possibly except for ν*, where δ(G) is the minimum degree of G and κ′(G) is the edge-connectivity of G. In addition, we show that the results in this paper are best possible and a polynomial time algorithm can be obtained for actually finding such a partition by our proof.     

单循环赛赛程安排的一个图论方法

利用图论的边着色理论建立了一个赛程安排的数学模型 .首先建立 n支球队与完全图 Kn的 n个顶点间的一一对应 ,把球队 Ai和 Aj间的比赛关系抽象成 Kn的顶点 i和 j间的边 ( i,j) .然后分别构造出了图K2 m- 1和 K2 m的正常 2 m-1边着色 .从而给出了各球队每两场比赛间得到的休整时间最均等 ,休整的间隔场次数达到上限值 n2 的一个赛程安排方案     

θ*r,s,t-图与唯一2-列表染色图的特征化

如果一个图G存在一个k-列表安排使得G具有一个唯一列表染色,则称 G是唯一列表可染色图,简称UkLC图．我们称图G具有M(k)性质当且仅当G不 是UkLC图．本文在借鉴θr,s,t-图概念的基础上引入θr,s,t-图的定义,并证明:除了 r=s=t=2以外,θr,s,t-图都是U2LC图．利用如上结果我们给出M．Mahdian and E．S．Mahmoodian对U2LC图所作特征化的一个简单证明．     

反超图的笛卡儿积的上色数

讨论反超图的笛卡儿积的着色理论 ,求出了满足一定条件的反超图的笛卡儿积的上色数 .     

Coloring mixed hypertrees

A mixed hypergraph is a triple (V,C,D) where V is its vertex set and C and D are families of subsets of V, called C-edges and D-edges, respectively. For a proper coloring, we require that each C-edge contains two vertices with the same color and each D-edge contains two vertices with different colors. The feasible set of a mixed hypergraph is the set of all k's for which there exists a proper coloring using exactly k colors. A hypergraph is a hypertree if there exists a tree such that the edges of the hypergraph induce connected subgraphs of the tree.We prove that feasible sets of mixed hypertrees are gap-free, i.e., intervals of integers, and we show that this is not true for precolored mixed hypertrees. The problem to decide whether a mixed hypertree can be colored by k colors is NP-complete in general; we investigate complexity of various restrictions of this problem and we characterize their complexity in most of the cases.     

具有唯一4度最大度点的图的全色数

一个图Ｇ的全色数χ_T（Ｇ）是使得Ｖ（Ｇ）∪Ｅ（Ｇ）中相邻或相关联元素均染不同颜色的最少颜色数．文中证明了，若图Ｇ只有唯一的一个４度最大度点，则χ_T（Ｇ）＝Δ（Ｇ）＋１．     

Improved square coloring of planar graphs

Square coloring is a variant of graph coloring where vertices within distance two must receive different colors. When considering planar graphs, the most famous conjecture (Wegner, 1977) states that $\frac{3}{2}\mathrm{\Delta }+1$ colors are sufficient to square color every planar graph of maximum degree Δ. This conjecture has been proven asymptotically for graphs with large maximum degree. We consider here planar graphs with small maximum degree and show that $2\mathrm{\Delta }+7$ colors are sufficient, which improves the best known bounds when $6?\mathrm{\Delta }?31$.