论文标题
约翰逊图的集团结构
The Clique Structure of Johnson Graphs
论文作者
论文摘要
这项工作是由赫利和奥尔德福德（2011）中给出的高维统计数据可视化的方法的动机，研究了$ j_n（M，M，M-1）$ JOHNSON GRAPHS的集团结构。集团和最大集团的特征是，并被证明是仅有的两种类型之一。这些类型的特征是相交的特征和[n] = {1，2，...，n}子集的联合的特征，该子集定义了图的顶点。集团数字和集团分区编号如下。约翰逊图的结果与与极端集理论相关的集合家族的结果连接。
Motivated by an approach to visualization of high dimensional statistical data given in Hurley and Oldford (2011), this work examines the clique structure of $J_n(m, m-1)$ Johnson graphs. Cliques and maximal cliques are characterized and proved to be of one of only two types. These types are characterized by features of the intersection and of the union of the subsets of [n] = {1, 2, ..., n} which define the vertices of the graph. Clique numbers and clique partition numbers follow. The results on Johnson graphs are connected to results on intersecting families of sets related to extremal set theory.
