منابع مشابه
On two classes of nearly binary matroids
We give an excluded-minor characterization for the class of matroids M in which M\e or M/e is binary for all e in E(M). This class is closely related to the class of matroids in which every member is binary or can be obtained from a binary matroid by relaxing a circuithyperplane. We also provide an excluded-minor characterization for the second class.
متن کاملClasses of Matroids
This paper explores which classes of graphs and matroids are k-balanced. A connection between k-balanced graphs and k-balanced matroids was also obtained. In this paper, we continue our study of the class of k-balanced matroids in order to see what matroid operations preserve k-balance. Since strong maps of matroids are defined as analogues of continuous maps of topological spaces, it is natura...
متن کاملOn bipartite restrictions of binary matroids
In a 1965 paper, Erdős remarked that a graph G has a bipartite subgraph that has at least half the number of edges of G. The purpose of this note is to prove a matroid analogue of Erdős’s original observation. It follows from this matroid result that every loopless binary matroid has a restriction that uses more than half of its elements and has no odd circuits; and, for 2 ≤ k ≤ 5, every bridge...
متن کاملOn the circuit-spectrum of binary matroids
Murty, in 1971, characterized the connected binary matroids with all circuits having the same size. We characterize the connected binary matroids with circuits of two different sizes, where the largest size is odd. As a consequence of this result we obtain both Murty’s result and other results on binary matroids with circuits of only two sizes. We also show that it will be difficult to complete...
متن کاملOn removable series classes in connected matroids
A series class P of a connected matroid M is removable if M \ P is connected. In this paper, we prove that a connected matroid M with r(M) ≥ 2 has at least r(M) + 1 removable series classes. Further, we obtain certain results from which the following result of Oxley and its graph theoretic version follow: If C is a circuit of a connected matroid M with C 6= M such that M \ x is not connected fo...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2014
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2013.07.017