Add to ORKGA result of Seymour implies that any 3-connected matroid with a modular 3-point line is binary. We prove a similar characterization for 3-connected matroids with modular 4-point lines. We show that such a matroid is either representable over GF(3) or GF(4) or has an F7-minor and either an
AbstractIn this paper, we construct all 3-connected binary matroids with circumference equal to 6 or...
The cycle matroids of wheels are the fundamental building blocks for the class of binary matroids. B...
AbstractD.W. Hall proved that every simple 3-connected graph with a K5-minor must have a K3.3-minor,...
It was proved by Oxley that U2,4 is the only non-trivial 3-connected matroid N such that, whenever a...
Abstract. Let AG(3, 2) 1 U1,1 denote the binary matroid obtained from AG(3, 2)⊕U1,1 by completing th...
AbstractWe prove that an internally 4-connected binary matroid with no minor isomorphic to M(K3,3),M...
AbstractA collection F of 3-connected matroids is triangle-rounded if, whenever M is a 3-connected m...
AbstractA result of Walton and the author establishes that every 3-connected matroid of rank and cor...
AbstractWe prove that if M is an internally 4-connected binary matroid with an M(K5)-minor and with ...
AbstractBrylawski identified the class of binary matroids with no minor isomorphic to M(K4) as being...
In this paper, we give a complete characterization of binary matroids with no P9-minor. A 3-connecte...
AbstractWe show that if X is a five-element line in a 3-connected matroid M which has a six-element ...
AbstractWe prove that every internally 4-connected non-regular binary matroid other than F7 and F7∗ ...
We show that for every n ≥ 3 there is some number m such that every 4-connected binary matroid with ...
AbstractA matroid M is called minor-minimally 3-connected if M is 3-connected and, for each e∈E(M), ...
AbstractIn this paper, we construct all 3-connected binary matroids with circumference equal to 6 or...
The cycle matroids of wheels are the fundamental building blocks for the class of binary matroids. B...
AbstractD.W. Hall proved that every simple 3-connected graph with a K5-minor must have a K3.3-minor,...
It was proved by Oxley that U2,4 is the only non-trivial 3-connected matroid N such that, whenever a...
Abstract. Let AG(3, 2) 1 U1,1 denote the binary matroid obtained from AG(3, 2)⊕U1,1 by completing th...
AbstractWe prove that an internally 4-connected binary matroid with no minor isomorphic to M(K3,3),M...
AbstractA collection F of 3-connected matroids is triangle-rounded if, whenever M is a 3-connected m...
AbstractA result of Walton and the author establishes that every 3-connected matroid of rank and cor...
AbstractWe prove that if M is an internally 4-connected binary matroid with an M(K5)-minor and with ...
AbstractBrylawski identified the class of binary matroids with no minor isomorphic to M(K4) as being...
In this paper, we give a complete characterization of binary matroids with no P9-minor. A 3-connecte...
AbstractWe show that if X is a five-element line in a 3-connected matroid M which has a six-element ...
AbstractWe prove that every internally 4-connected non-regular binary matroid other than F7 and F7∗ ...
We show that for every n ≥ 3 there is some number m such that every 4-connected binary matroid with ...
AbstractA matroid M is called minor-minimally 3-connected if M is 3-connected and, for each e∈E(M), ...
AbstractIn this paper, we construct all 3-connected binary matroids with circumference equal to 6 or...
The cycle matroids of wheels are the fundamental building blocks for the class of binary matroids. B...
AbstractD.W. Hall proved that every simple 3-connected graph with a K5-minor must have a K3.3-minor,...