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Spanning cycles in regular matroids without small cocircuits. (English) Zbl 1248.05030
Summary: A cycle of a matroid is a disjoint union of circuits. A cycle $$C$$ of a matroid $$M$$ is spanning if the rank of $$C$$ equals the rank of $$M$$. Settling an open problem of D. Bauer [Congr. Numerantium 49, 11–18 (1985; Zbl 0621.05021)], P. A. Catlin [J. Graph Theory 12, No. 1, 29–44 (1988; Zbl 0659.05073)] showed that if $$G$$ is a 2-connected graph on $$n>16$$ vertices, and if $$\delta(G)>\frac {n}{5}-1$$, then $$G$$ has a spanning cycle. Catlin also showed that the lower bound of the minimum degree in this result is best possible. In this paper, we prove that for a connected simple regular matroid $$M$$, if for any cocircuit $$D$$, $$|D|\geq$$ max$$\{\frac {r(M)-4}{5},6\}$$, then $$M$$ has a spanning cycle.

MSC:
 05B35 Combinatorial aspects of matroids and geometric lattices
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References:
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