论文标题
具有块大小3的对称配置的着色问题
Colouring problems for symmetric configurations with block size 3
论文作者
论文摘要
对称配置的研究$ v_3 $具有块尺寸3的历史悠久。在本文中，我们考虑了在研究这些结构中自然出现的两个着色问题。其中的第一个是弱的着色，其中没有块是单色的。第二个是强烈的着色，其中每个块都是多色的。前者之前已经研究了有关阻塞集的研究。结果证明了阻塞集的可能大小，我们开始研究强颜色。我们还表明，没有阻塞集的已知$ 21_3 $和$ 22_3 $配置是唯一的，并且可以完全枚举所有非iSomorphic $ 20_3 $配置。我们讨论了与对称配置有关的连接概念，并完成了2个连接的对称配置的频谱，而无需阻止集合。提出了许多开放问题。
The study of symmetric configurations $v_3$ with block size 3 has a long and rich history. In this paper we consider two colouring problems which arise naturally in the study of these structures. The first of these is weak colouring, in which no block is monochromatic; the second is strong colouring, in which every block is multichromatic. The former has been studied before in relation to blocking sets. Results are proved on the possible sizes of blocking sets and we begin the investigation of strong colourings. We also show that the known $21_3$ and $22_3$ configurations without a blocking set are unique and make a complete enumeration of all non-isomorphic $20_3$ configurations. We discuss the concept of connectivity in relation to symmetric configurations and complete the determination of the spectrum of 2-connected symmetric configurations without a blocking set. A number of open problems are presented.
