The structure of the 4-separations in 4-connected matroids |
| |
Authors: | Jeremy Aikin |
| |
Institution: | a Mathematics Department, Macon State College, Macon, GA 31206, United States b Mathematics Department, Louisiana State University, Baton Rouge, LA 70803-4918, United States |
| |
Abstract: | For a 2-connected matroid M, Cunningham and Edmonds gave a tree decomposition that displays all of its 2-separations. When M is 3-connected, two 3-separations are equivalent if one can be obtained from the other by passing through a sequence of 3-separations each of which is obtained from its predecessor by moving a single element from one side of the 3-separation to the other. Oxley, Semple, and Whittle gave a tree decomposition that displays, up to this equivalence, all non-trivial 3-separations of M. Now let M be 4-connected. In this paper, we define two 4-separations of M to be 2-equivalent if one can be obtained from the other by passing through a sequence of 4-separations each obtained from its predecessor by moving at most two elements from one side of the 4-separation to the other. The main result of the paper proves that M has a tree decomposition that displays, up to 2-equivalence, all non-trivial 4-separations of M. |
| |
Keywords: | 05B35 |
本文献已被 ScienceDirect 等数据库收录! |
|