TY - JOUR
T1 - Excluding Kuratowski graphs and their duals from binary matroids
AU - Mayhew, Dillon
AU - Royle, Gordon
AU - Whittle, Geoff
PY - 2017/7/1
Y1 - 2017/7/1
N2 - We consider some applications of our characterisation of the internally 4-connected binary matroids with no M(K3,3)-minor. We characterise the internally 4-connected binary matroids with no minor in M, where M is a subset of {M(K3,3),M⁎(K3,3),M(K5),M⁎(K5)} that contains either M(K3,3) or M⁎(K3,3). We also describe a practical algorithm for testing whether a binary matroid has a minor in M. In addition we characterise the growth-rate of binary matroids with no M(K3,3)-minor, and we show that a binary matroid with no M(K3,3)-minor has critical exponent over GF(2) at most equal to four.
AB - We consider some applications of our characterisation of the internally 4-connected binary matroids with no M(K3,3)-minor. We characterise the internally 4-connected binary matroids with no minor in M, where M is a subset of {M(K3,3),M⁎(K3,3),M(K5),M⁎(K5)} that contains either M(K3,3) or M⁎(K3,3). We also describe a practical algorithm for testing whether a binary matroid has a minor in M. In addition we characterise the growth-rate of binary matroids with no M(K3,3)-minor, and we show that a binary matroid with no M(K3,3)-minor has critical exponent over GF(2) at most equal to four.
KW - Binary matroid
KW - Critical exponent
KW - Growth-rate
KW - Internally 4-connected
KW - Kuratowski graphs
UR - http://www.scopus.com/inward/record.url?scp=85015927950&partnerID=8YFLogxK
U2 - 10.1016/j.jctb.2017.03.005
DO - 10.1016/j.jctb.2017.03.005
M3 - Article
AN - SCOPUS:85015927950
SN - 0095-8956
VL - 125
SP - 95
EP - 113
JO - Journal of Combinatorial Theory. Series B
JF - Journal of Combinatorial Theory. Series B
ER -