## Computing the Excluded Minors for Branch-Width 3 over Small Fields

This is an online addition to the paper
[Petr Hlineny,
*On the Excluded Minors for Matroids of Branch-Width Three*,
submitted 2002],
using the **MACEK matroid computing package**.
### Binary Excluded Minors

We provide a computer-assisted proof for the following finite-case statement:
**Lemma 4.4**
Let M be a 3-connected binary matroid on at most 14 elements
with an F_{7}-minor.
If M has branch-width 4, then M has an N-minor
for some N in *F*_{2}.

Here *F*_{2}
= {grQ3, grO6, grK5, grK5*, grV8, grV8*, R10, ND11, ND14, ND23}.

For the proof we use a Macek procedure bw3bin
provided for download.
This procedure and its use is extensively described here.

### Ternary Excluded Minors

We provide a computer-assisted proof for the following finite-case statement:
**Proposition 4.5**
Let *F*_{3} be the set of (pairwise non-isomorphic) excluded
minors for branch-width 3 that are ternary but not binary.
Then *F*_{3} contains no matroids on less than 9 elements,
18 matroids on 9 elements,
31 matroids on 10 elements,
and no matroid on 11 or 12 elements.

The set *F*_{3} on up to 12 elements is
here,
and a Macek procedure bw3tern here.
This procedure and its use is extensively described here.

### Quaternary Excluded Minors

We provide a computer-assisted proof for the following finite-case statement:
**Proposition 4.6**
Let *F*_{4} be the set of (pairwise non-isomorphic) excluded
minors for branch-width 3 that are quaternary but neither ternary nor binary.
Then *F*_{4} contains no matroids on less than 8 elements,
5 matroids on 8 elements,
90 matroids on 9 elements,
and 32 matroids on 10 elements.

The set *F*_{4} on up to 10 elements is
here,
and a Macek procedure bw3quat here.
This procedure and its use is extensively described here.

Copyright (C) 2001,2002 Petr Hlineny,

Petr.Hlineny!nosp@m!vuw.ac.nz or Petr.Hlineny!nosp@m!seznam.cz

This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.

You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA.