Name
Abstract | ||
|---|---|---|
Let N be a matroid with k connected components and M be a minor-minimal connected matroid having N as a minor. This note proves that | E ( M ) − E ( N )| is at most 2 k − 2 unless N or its dual is free, in which case | E ( M ) − E ( N )| ⩽ k − 1. Examples are given to show that these bounds are best possible for all choices for N . A consequence of the main result is that a minimally connected matroid of rank r and maximum circuit size c has at most 2 r − c + 2 elements. This bound sharpens a result of Murty. |
Year | DOI | Venue |
|---|---|---|
1998 | 10.1016/S0012-365X(98)00055-7 | Discrete Mathematics |
Keywords | Field | DocType |
connected matroids,05b35,connected component | Matroid,Discrete mathematics,Combinatorics,Connected component,Mathematics | Journal |
Volume | Issue | ISSN |
189 | 1-3 | Discrete Mathematics |
Citations | PageRank | References |
10 | 1.20 | 3 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Manoel Lemos | 1 | 83 | 19.44 |
| James Oxley | 2 | 397 | 57.57 |