We consider the $\mathrm{GF}(4)$-representable matroids with a circuit-hyperplane such that the matroid obtained by relaxing the circuit-hyperplane is also $\mathrm{GF}(4)$-representable. We characterize the structure of these matroids as an application of structure theorems for the classes of $U_{2,4}$-fragile and $\{U_{2,5},U_{3,5}\}$-fragile matroids. In addition, we characterize the forbidden submatrices in $\mathrm{GF}(4)$-representations of these matroids.
@article{10_37236_6959,
author = {Ben Clark and James Oxley and Stefan H.M. van Zwam},
title = {Relaxations of {\(\mathrm{GF}(4)\)-representable} matroids},
journal = {The electronic journal of combinatorics},
year = {2018},
volume = {25},
number = {2},
doi = {10.37236/6959},
zbl = {1391.05072},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6959/}
}
TY - JOUR
AU - Ben Clark
AU - James Oxley
AU - Stefan H.M. van Zwam
TI - Relaxations of \(\mathrm{GF}(4)\)-representable matroids
JO - The electronic journal of combinatorics
PY - 2018
VL - 25
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/6959/
DO - 10.37236/6959
ID - 10_37236_6959
ER -
%0 Journal Article
%A Ben Clark
%A James Oxley
%A Stefan H.M. van Zwam
%T Relaxations of \(\mathrm{GF}(4)\)-representable matroids
%J The electronic journal of combinatorics
%D 2018
%V 25
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/6959/
%R 10.37236/6959
%F 10_37236_6959
Ben Clark; James Oxley; Stefan H.M. van Zwam. Relaxations of \(\mathrm{GF}(4)\)-representable matroids. The electronic journal of combinatorics, Tome 25 (2018) no. 2. doi: 10.37236/6959
