若干图类的邻强边染色

研究了若干图类的邻强边染色 .利用在图中添加辅助点和边的方法 ,构造性的证明了对于完全图 Kn和路 Lm 的笛卡尔积图 Kn× Lm,有χ′as(Kn× Lm) =△ (Kn× Lm) +1 ,其中△ (Kn× Lm)和χ′as(Kn× Lm)分别表示图 Kn× Lm的最大度和邻强边色数 .同理验证了 n阶完全图 Kn的广义图 K(n,m)满足邻强边染色猜想 .     

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．     

Halin-图的点强全染色

图G(V,E)的一个k-正常全染色f叫做一个k-点强全染色当且仅当对任意v∈V(G), N[v]中的元素被染不同色,其中N[v]={u|uv∈V(G)}∪{v}．χTvs(G)=min{k|存在图G的k- 点强全染色}叫做图G的点强全色数．对3-连通平面图G(V,E),如果删去面fo边界上的所有点后的图为一个树图,则G(V,E)叫做一个Halin-图．本文确定了最大度不小于6的Halin- 图和一些特殊图的的点强全色数XTvs(G),并提出了如下猜想:设G(V,E)为每一连通分支的阶不小于6的图,则χTvs(G)≤△(G) 2,其中△(G)为图G(V,E)的最大度．     

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     

Using graphs for some discrete tomography problems

Given a rectangular array whose entries represent the pixels of a digitalized image, we consider the problem of reconstructing an image from the number of occurrences of each color in every column and in every row. The complexity of this problem is still open when there are just three colors in the image. We study some special cases where the number of occurrences of each color is limited to small values. Formulations in terms of edge coloring in graphs and as timetabling problems are used; complexity results are derived from the model.     

New Results on the Queens_n 2 Graph Coloring Problem

For the Queens_n ² graph coloring problems no chromatic numbers are available for n > 9 except where n is not a multiple of 2 or 3. In this paper we propose an exact algorithm that takes advantage of the particular structure of these graphs. The algorithm works on the independent sets of the graph rather than on the vertices to be colored. It combines branch and bound, for independent set assignment, with a clique based filtering procedure. A first experimentation of this approach provided the coloring number values ranging for n = 10 to n = 14.