1School of Mathematics and Statistics, University of Canterbury 2Mathematics Department, Louisiana State University 3School of Mathematics, University of Bristol and Heilbronn Institute for Mathematical Research 4Louisiana State University
The electronic journal of combinatorics, Tome 27 (2020) no. 3
One characterization of binary matroids is that the symmetric difference of every pair of intersecting circuits is a disjoint union of circuits. This paper considers circuit-difference matroids, that is, those matroids in which the symmetric difference of every pair of intersecting circuits is a single circuit. Our main result shows that a connected regular matroid is circuit-difference if and only if it contains no pair of skew circuits. Using a result of Pfeil, this enables us to explicitly determine all regular circuit-difference matroids. The class of circuit-difference matroids is not closed under minors, but it is closed under series minors. We characterize the infinitely many excluded series minors for the class.
George Drummond
1
;
Tara Fife
2
;
Kevin Grace
3
;
James Oxley
4
1
School of Mathematics and Statistics, University of Canterbury
2
Mathematics Department, Louisiana State University
3
School of Mathematics, University of Bristol and Heilbronn Institute for Mathematical Research
4
Louisiana State University
@article{10_37236_9314,
author = {George Drummond and Tara Fife and Kevin Grace and James Oxley},
title = {Circuit-difference matroids},
journal = {The electronic journal of combinatorics},
year = {2020},
volume = {27},
number = {3},
doi = {10.37236/9314},
zbl = {1465.05027},
url = {http://geodesic.mathdoc.fr/articles/10.37236/9314/}
}
TY - JOUR
AU - George Drummond
AU - Tara Fife
AU - Kevin Grace
AU - James Oxley
TI - Circuit-difference matroids
JO - The electronic journal of combinatorics
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George Drummond; Tara Fife; Kevin Grace; James Oxley. Circuit-difference matroids. The electronic journal of combinatorics, Tome 27 (2020) no. 3. doi: 10.37236/9314
