On bound graphs and simplicial vertices

我们考虑了上界图、双界图和半界图的单纯顶点和非极大团覆盖。利用这些性质，我们得到了半有界图的一些特征。我们还处理偏序集之间的转换，其半有界图是相同的。得到了具有相同双标准偏序集和相同半有界图两个偏序集之间距离的上界。11基于单纯顶点的性质，我们得到了上界图的一个构造方法，并利用禁止子图和禁止子集来研究上界图和双界图。讨论了子图所对应的子集的一些性质。利用团覆盖和单纯顶点的概念，得到了无三角形子图的一些性质。利用这些结果，我们得到了分裂双界图、阈值双界图和差界图的禁用子图和子偏序集的刻画。

We consider upper bound graphs, double bound graphs and semi bound graphs in terms of simplicial vertices and non-maximal clique covers. Using these properties, we obtain some characterization of semi bound graphs. We also deal with transformations between posets whose semi bound graphs are the same. We obtain that upper bound of distances between two posets with the same double canonical poset and the same semi bound graph. Based on properties of simplicial vertices, we obtain a construction method of upper bound graphsWe also consider upper bound graphs and double bound graphs in terms of forbidden subgraphs and forbidden subposets. We deal with some properties on subposets corresponding to subgraphs. We obtain some properties on m-subposets, (n,m)-subposets and induced subgraphs.Using concepts of clique covers and simplicial vertices, we obtain some properties on triangle-free subgraphs. By these results, we obtain characterizations of split double bound graphs, threshold double bound graphs and difference bound graphs in terms of forbidden subgraphs and subposets.