关于图的L(d1,d2)-标号问题

图的L(2,1)-标号问题是由频率分配问题归结而来,本文研究作为L(2,1)-标号问题的推广的L(d_1,d_2)-标号问题。首先定义了顶点2-着色,2-色数及其它有关概念,给出了2-色数的上界。然后得出了λ_(d_1,d_2)(G)与δ(G)和Δ(G)的一般关系。最后得出了一般图与平面图的λ_(d_1,d_2)(G)的上界。     

Discussion No. 2

The original version of the half-normal plot [C. Daniel, Technometrics, t, (1959), 311–34] is reviewed and two modified versions are introduced. The modified versions incorporate corrections of a major flaw in the original version relating to critical values and a minor flaw relating to plotting positions. The critical values given in this article control the probability error rate, the probability of at least one false positive in the analysis of an experiment, and are considerably different from those given by Daniel. One of the modified versions is more powerful than Daniel's original procedure. Anothe improvement made in the modified versions is that only the smallest 70%, of the contrasts not declared significant, are used to constuct the final estimate of the error variance. This results in an appreciable redaction in the mean square error of this estimate. Examples are plesented to illustrate the use of the various half-normal plot versions.