A Note on Dominating Circuits of Splitting Off Matroids

In 1971, nash-williams proved that if g is a simple 2-connected graph on n vertices having minimumdegree at least 1/3(n+2), then any longest cycle c in g is also edge-dominating; that is, each edge ofg has at least one end-vertex incident with a vertex of c. we say that a circuit c in a matroid m isdominating if each component of m/c has rank at most one. in this paper, we generalize the dominatingcircuits in matroids and also we prove that all dominating circuits is not dominating circuits in splittingoff matroids