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

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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.