k-方体图邻点可区别全色数

本文证明k-方体图(k≥2)的邻点可区别的全色数为k+2.     

若干图的点强全染色(英文)

对图G及正整数k，映射f：满足：（1）任意e1，e3，如果e1，e2是相邻或相关联的，则有；（2）对u，v，w（G）有，则称f为G的一个k-点强全染色，并且K|G的社点强全染色称为G的点强全色数．本文讨论了一些特殊困的点强全色数，并提出了一个猜想：若G为每一分图的阶数不小于6的图，则（G），其中（G）为本文中定义的一新参数．     

水性颜料体系无树脂色浆的制备与应用

中性墨水属于热力学上不稳定的颜料悬浮体系,选择低黏度、高稳定性的色浆是保证墨水体系分散稳定性的重要手段之一。基于此,以颜料炭黑和酞菁蓝为着色剂,配合超分散剂(EK43)与协同增效剂(BM10),制备了两款适用于中性墨水体系的无树脂色浆。首次从色浆粒径与体系分散稳定性角度出发,确定了EK43、BM10用量以及最佳研磨时间,并对其理化性能、稳定性与书写性能进行分析测试。结果表明:在黑色浆中添加质量分数10.0%的EK43、2.5%的BM10,研磨时间为90 min;在蓝色浆中添加质量分数8.0%的EK43、2.0%的BM10,研磨时间为120 min时,两种色浆的粒径与分散稳定性均达到最佳。所制备的无树脂色浆颜料固含量高、黏度较低、储存稳定性好、着色力强,以其调配的中性墨水书写性能良好,且具有较好的离心稳定性和耐热稳定性。     

Scheduling Problems and Mixed Graph Colorings

Some scheduling problems induce a mixed graph coloring, i.e., an assignment of positive integers (colors) to vertices of a mixed graph such that, if two vertices are joined by an edge, then their colors have to be different, and if two vertices are joined by an arc, then the color of the startvertex has to be not greater than the color of the endvertex. We discuss some algorithms for coloring the vertices of a mixed graph with a small number t of colors and present computational results for calculating the chromatic number, i.e., the minimal possible value of such a t . We also study the chromatic polynomial of a mixed graph which may be used for calculating the number of feasible schedules.     

乘积图的全色数

本文得到了有关乘积图的全色数的一些结果，并利用这些结果证明了Mesh图和Tours-图均满足全色数猜想．特别，几乎所有的Mesh-图都是第一类图．     

非平面图的色数算法

本文对非平面无向简单图的点着色问题进行分析研究后,提出了一个点色数算法.该算法不仅给出了非平面图求点色数的方法,同时也解决了着色方法.并且对算法所涉及的有关性质定理给出了证明.     

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.     

Coloring axis-parallel rectangles

For every k and r, we construct a finite family of axis-parallel rectangles in the plane such that no matter how we color them with k colors, there exists a point covered by precisely r members of the family, all of which have the same color. For r=2, this answers a question of S. Smorodinsky [S. Smorodinsky, On the chromatic number of some geometric hypergraphs, SIAM J. Discrete Math. 21 (2007) 676-687].     

Backbone colorings of graphs with bounded degree

We study backbone colorings, a variation on classical vertex colorings: Given a graph G and a subgraph H of G (the backbone of G), a backbone coloring for G and H is a proper vertex k-coloring of G in which the colors assigned to adjacent vertices in H differ by at least 2. The minimal k∈N for which such a coloring exists is called the backbone chromatic number of G. We show that for a graph G of maximum degree Δ where the backbone graph is a d-degenerated subgraph of G, the backbone chromatic number is at most Δ+d+1 and moreover, in the case when the backbone graph being a matching we prove that the backbone chromatic number is at most Δ+1. We also present examples where these bounds are attained.Finally, the asymptotic behavior of the backbone chromatic number is studied regarding the degrees of G and H. We prove for any sparse graph G that if the maximum degree of a backbone graph is small compared to the maximum degree of G, then the backbone chromatic number is at most .