A matroid circuit is a minimal dependent subset of a matroid. Every proper subset of a matroid circuit is independent. The family of matroid circuits determines the matroid. In a graphic matroid, the matroid circuits are the edge sets of graph cycles. A matroid circuit of the dual matroid is a matroid cocircuit of the original matroid (Fu 2026).
Matroid Circuit
See also
Circuit-Cocircuit Intersection Conjecture, Dual Matroid, Graphic Matroid, Matroid, Matroid CocircuitExplore with Wolfram|Alpha
References
Fu, H. "A Counterexample to the Circuit-Cocircuit Intersection Conjecture." 5 Oct 2026. https://arxiv.org/abs/2610.06033.Cite this as:
Weisstein, Eric W. "Matroid Circuit." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MatroidCircuit.html