Mathematical Sciences: A Decomposition Theory for 3-Connected Graphs and Matroids

数学科学：三连通图和拟阵的分解理论

• 批准号: 9308502
• 负责人: Leah Gardner
• 金额: $ 1.8万
• 依托单位: University of Indianapolis
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-08-01 至 1995-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9308502&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Decomposition; Theory; Connected

The proposed research will extend the decomposition theory of 3-connected graphs in three areas. First, classes of well-structured graphs related to a Coullard-Gardner-Wagner decomposition will be characterized by simple, well-defined replacements and excluded minor theorems. Second, algorithmic results will be obtained on these classes. Third, the decomposition theory of 3-connected graphs will be extended to 3-connected matroids.

本文的研究将3连通图的分解理论扩展到三个方面。首先，与库拉德-加德纳-瓦格纳分解相关的结构良好的图类将用简单的、定义良好的替换和排除的次要定理来表征。其次，将在这些类上获得算法结果。第三，将3连通图的分解理论推广到3连通拟阵。