On subgraphs and subposets of bound graphs

我们考虑上界图和双界图的诱导子图和子偏序集。利用团覆盖讨论了有界图的诱导子图与子偏序集之间的关系，并基于双有界图的团覆盖的性质，讨论了具有相同半有界图的偏序集族的极大偏序集和极小偏序集的性质.我们得到了具有相同半有界图的偏序集族的直径和半径，并考虑了k-树的叶数。我们证明了对于给定的叶数存在k-树，并讨论了主序理想和区间的性质。利用这些性质，我们考虑家庭的集团禁止子图。利用禁止上界子图的概念，得到了几类上界图的子族的特征。例如，星星n-图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，G及其补图是Meyniel图当且仅当G不包含C_5、P_5和House图作为导出子图。

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.