On bound graphs and simplicial vertices

我们从简单顶点和非极大团盖的角度考虑上界图、双界图和半界图。利用这些性质，我们得到了半有界图的一些刻画。我们也处理半界图相同的偏序集之间的变换。我们得到了具有相同双正则序集和相同半界图的两个序集之间距离的上界。基于简单顶点的性质，给出了上界图的构造方法，并从禁止子图和禁止传票集的角度考虑上界图和双界图。我们处理了与子图相对应的传票集上的一些性质。得到了m-传票集、(n,m)-传票集和诱导子图的一些性质。利用团盖和简单顶点的概念，得到了无三角形子图的一些性质。通过这些结果，我们得到了分割双界图、阈值双界图和差分双界图在禁止子图和传票集上的刻画。

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.