Name
Abstract | ||
|---|---|---|
We examine the specialization to simple matroids of certain problems in extremal matroid theory that are concerned with bounded cocircuit size. Assume that each cocircuit of a simple matroid M has at most d elements. We show that if M has rank 3, then M has at most d + ⌊√d⌋ + 1 points, and we classify the rank-3 simple matroids M that have exactly d + ⌊√d⌋ points. We show that if M is a connected matroid of rank 4 and d is q3 with q 1, then M has at most q3 + q2 + q + 1 points; this upper bound is strict unless q is a prime power, in which case the only such matroid with exactly q3 + q2 + q + 1 points is the projective geometry PG(3, q). We also show that if d is q4 for a positive integer q and if M has rank 5 and is vertically 5-connected, then M has at most q4 + q3 + q2 + q + 1 points; this upper bound is strict unless q is a prime power, in which case PG(4, q) is the only such matroid that attains this bound. |
Year | DOI | Venue |
|---|---|---|
2000 | 10.1017/S0963548300004429 | Combinatorics, Probability & Computing |
Keywords | Field | DocType |
case pg,bounded cocircuit size,connected matroid,positive integer q,simple matroids,extremal matroid theory,prime power,simple matroid,certain problem,rank-3 simple matroids m | Integer,Matroid,Discrete mathematics,Combinatorics,Projective geometry,Upper and lower bounds,Matroid partitioning,Graphic matroid,Prime power,Mathematics,Bounded function | Journal |
Volume | Issue | ISSN |
9 | 5 | 0963-5483 |
Citations | PageRank | References |
0 | 0.34 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Joseph E. Bonin | 1 | 53 | 16.74 |
| Talmage James Reid | 2 | 48 | 12.18 |