On bound graphs and non-maximal cliques

我们利用非极大团覆盖、区间和序理想来研究上界图、双界图和半界图。利用这些性质，我们得到了双界图和半界图的一些性质，并利用非极大团的性质，研究了无限偏序集上的上界图和双界图的一些性质。研究了无限树偏序集的上界图和双界图的性质，得到了这类图的特征，利用界图的遗传性概念，得到了几类遗传界图的一些性质.利用这些结果，我们得到了遗传上界图、遗传双界图和遗传半界图的禁忌子图和禁忌子集的刻画。我们还研究了与禁止子图对应的子偏序集的一些性质，讨论了具有相同上界图的偏序集族的极大偏序集和极小偏序集的一些性质。我们还考虑了上界图相同的偏序集之间的变换。得到了具有相同标准偏序集和相同上界图的两个偏序集可以通过两个变换的有限序列相互变换，即x<y-加法和x<y-消去.

We consider upper bound graphs, double bound graphs and semi bound graphs in terms of non-maximal clique covers, intervals and order ideals. Using these properties, we obtain some characterization of double bound graphs and semi bound graphs.Based on properties of non-maximal cliques, we deal with some properties of upper bound graphs and double bound graphs on infinite posets. We consider properties on upper bound graphs and double bound graphs of infinite tree posets and obtain characterizations of these graphs.Using concepts of hereditariness of bound graphs, we obtain some properties on some kinds of hereditary bound graphs. By these results, we obtain characterizations of hereditary upper bound graphs, hereditary double bound graphs and hereditary semi bound graphs in terms of forbidden subgraphs and subposets. We also consider some properties on subposets corresponding forbidden subgraphs.We deal with properties on maximal posets and minimal posets of a poset family with same upper bound graph. We also consider transformations between posets whose upper bound graphs are the same. We obtain that two posets with the same canonical poset and the same upper bound graph can be transformed into each other by a finite sequence of two transformations, that is, x<y-additions and x<y-deletions.