On subgraphs and subposets of bound graphs

我们从诱导子图和传票集的角度考虑上界图和双界图。我们还从团覆盖的角度讨论了界图的诱导子图和传票集之间的关系。在双界图团盖性质的基础上，讨论了具有相同半界图的一个序集族的最大序集和最小序集的性质。我们得到了具有相同半界图的序集族的直径和半径。我们也用叶子来考虑k树。我们证明存在一个k树对于给定的叶数。我们处理关于主序理想和区间的性质。利用这些性质，我们考虑了禁止子图上的团族。我们用禁止上界子图的形式得到了一些上界图亚族的刻画。例如，星形n-gon是上界弦图的禁止上界子图。2K_2是上界分裂图的一个禁止上界子图。对于图G，当且仅当G不包含C_5， P_5和屋图作为诱导子图时，G及其补是梅尼埃尔图。

We consider upper bound graphs and double bound graphs in terms of induced subgraphs and subposets. We also deal with the relations between induced subgraphs and subposets of bound graphs in terms of clique covers.Based on properties of clique covers of double bound graphs, we deal with properties on maximal posets and minimal posets of a poset family with same semi bound graph. We obtain of the diameter and the radius of the family of posets with same semi bound graph.We also consider k-trees in terms of leafages. We show that there exists a k-tree for a given number of leafages.We deal with properties on principal order ideals and intervals. Using these properties, we consider families of cliques on forbidden subgraphs. We obtain characterizations of some kinds of subfamily of upper bound graphs in terms of forbidden upper bound subgraphs. For example, star n-gons are forbidden upper bound subgraphs of upper bound chordal graphs. 2K_2 is a forbidden upper bound subgraphs of upper bound split graphs. For a graph G, G and its complement are Meyniel graphs if and only if G does not contain C_5 , P_5 and the house graph as induced subgraphs.