Examples of matroid

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Our first result is an extremal matroid theorem where the prescribed property considered is bounded cocircuit size.
For this reason, we next discuss the matroid notion that generalizes the concept of a vertex in a graph.
Even if there exists an m-proof, it is not at all obvious how to search for a suitable matroid.
Since each loop in a matroid forms a one-element component, it suffices to prove the theorem for loopless matroids.
In the current section, this issue is expanded and it is shown that every matrix corresponds to a matroid.
To simplify the explanation, matroid theory is introduced in this paper using terminology of graph theory.
In graph theory terminology, a base is a spanning tree of the matroid.
The use of matroid theory to represent engineering systems is less known in the literature.
Also, it would be interesting to get further threshold sharpness results for the random matroid process.
Non-separating cocircuits of a matroid with two and three elements, respectively, are called vertex pairs and vertex triads.
In general, this dependence structure gives a matroid.
In a matroid, a triangle is a three-element circuit; a triad is a three-element cocircuit.
This leads to an efficient algorithm for generating a random basis of a balanced matroid approximately uniformly.
The resulting sum is a matroid represented on two intersecting planes in rank 4 (like the '3-dimensional' picture on the right).
Every matroid with a 2-transitive automorphism group is negatively correlated.
As a final comment, it is noted that the all of the results presented here have natural matroid generalizations.

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