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. Given a simple Eulerian binary matroid \ (M\), what is the minimum number of disjoint circuits necessary to decompose \ (M\)? We prove that \ (M / (rank (M) +1) \) many circuits suffice if \ (M = F₂ⁿ \0\\) is the complete binary matroid, for certain values of \ (n\), and that \ (O (2^rank (M) / (rank (M) +1) ) \) many circuits suffice for general \ (M\). We also determine the asymptotic behavior of the minimum number of circuits in an odd-cover of \ (M\). Keywordsbinary matroidmatroid circuitsarboricitycycle decompositionodd-coveringMSC codes05B3505C3805C70
Frederickson et al. (Mon,) studied this question.