Classification of subsets with minimal width and dual width in Grassmann, bilinear forms and dual polar graphs
Classification of subsets with minimal width and dual width in Grassmann, bilinear forms and dual polar graphs
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DOI：
10.1016/j.jcta.2005.08.006
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发表时间：
2006-07
期刊：
影响因子：
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通讯作者：
Hajime Tanaka
中科院分区：
文献类型：
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作者：
Hajime Tanaka
[多项式关联方案中子集的宽度和对偶宽度，J.Combin.理论系列。A 102(2003)255-271]分别在距离正则图和度量结合方案中引入了子集的宽度w和对偶宽度w*，并得到了这些新参数的下界。例如，在直径为d的度量距离正则图中，具有w+w*=d性质的子集达到这些界。本文对Grassmann图、双线性形式图和对偶极图中具有这一性质的子集进行了分类。利用这些信息，我们建立了前两类图的完全一般的ErdőS-Ko-Rado定理。
Brouwer, Godsil, Koolen and Martin [Width and dual width of subsets in polynomial association schemes, J. Combin. Theory Ser. A 102 (2003) 255–271] introduced the width w and the dual width w*of a subset in a distance-regular graph and in a cometric association scheme, respectively, and then derived lower bounds on these new parameters. For instance, subsets with the property w+w*=d in a cometric distance-regular graph with diameter d attain these bounds. In this paper, we classify subsets with this property in Grassmann graphs, bilinear forms graphs and dual polar graphs. We use this information to establish the Erdős–Ko–Rado theorem in full generality for the first two families of graphs.