On bound graphs and non-maximal cliques

关于有界图和非极大派

• 批准号: 14540137
• 负责人: TSUCHIYA Morimasa
• 金额: $ 2.62万
• 依托单位: TOKAI UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540137/
• 关键词: graph theory; poset; upper bound graph; double bound graph; semi bound graph

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.

我们从非极大团盖、区间和序理想等方面考虑上界图、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。基于非极大团的性质，讨论了无限偏集上的上界图和双界图的一些性质。研究了无限树序集的上界图和双界图的性质，得到了这些图的刻画。利用界图的遗传性概念，得到了几种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在禁止子图和召唤集上的刻画。我们还考虑了传票集对应的禁止子图上的一些性质。讨论了具有相同上界图的一类偏集族的极大偏集和极小偏集的性质。我们还考虑上界图相同的偏集之间的变换。我们得到了具有相同正则序集和相同上界图的两个序集可以通过两个变换的有限序列，即x<y-加法和x<y-删减，来相互变换。

项目成果

Morimasa Tsuchiya 他: "A Note on Hereditary Double Bound Graphs"Congressus Numerantium. 165. 123-127 (2003)

Morimasa Tsuchiya 等人：“关于遗传双界图的注释”Congressus Numerantium。165. 123-127 (2003)

Morimasa Tsuchiya 他: "Note on Double Bound Graphs of Infinite Posets"Southeast Asian Bulletin of Mathematics. 27. 599-602 (2003)

Morimasa Tsuchiya 等人：“关于无限命题的双界图的注释”东南亚数学公报 27. 599-602 (2003)

Morimasa Tsuchiya 他: "On Construction of Double Bound Graphs"Far East Journal of Applied Mathematics. 10. 161-168 (2003)

Morimasa Tsuchiya 等人：“论双界图的构造”远东应用数学杂志 10. 161-168 (2003)。

Morimasa Tsuchiya, Hiroshi Era, Kenjiro Ogawa: "Note on Double Bound Graphs of Infinite Posets"Southeast Asian Bulletin of Mathematics. 27. 599-602 (2003)

Morimasa Tsuchiya、Hiroshi Era、Kenjiro Okawa：“关于无限Posets的双界图的注释”东南亚数学公报。

Morimsa Tsuchiya, Kenjiro Ogawa, Shin-ichi Iwai: "On Construction of Double Bound Graphs"Far East Journal of Applied Mathematics. 10. 161-168 (2003)

Morimsa Tsuchiya、Kenjiro Okawa、Shin-ichi Iwai：“论双界图的构造”远东应用数学杂志。