For 0≤t≤r\documentclass[12pt]{minimal}
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\begin{document}$$0 \le t \le r$$\end{document} let m(t, r) be the maximum number s such that every t-edge-connected r-graph has s pairwise disjoint perfect matchings. There are only a few values of m(t, r) known, for instance m(3,3)=m(4,r)=1\documentclass[12pt]{minimal}
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\begin{document}$$m(3,3)=m(4,r)=1$$\end{document}, and m(t,r)≤r-2\documentclass[12pt]{minimal}
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\begin{document}$$m(t,r) \le r-2$$\end{document} for all t≠5\documentclass[12pt]{minimal}
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\begin{document}$$t \not = 5$$\end{document}, and m(t,r)≤r-3\documentclass[12pt]{minimal}
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\begin{document}$$m(t,r) \le r-3$$\end{document} if r is even. We prove that m(2l,r)≤3l-6\documentclass[12pt]{minimal}
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\begin{document}$$m(2l,r) \le 3l - 6$$\end{document} for every l≥3\documentclass[12pt]{minimal}
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\begin{document}$$l \ge 3$$\end{document} and r≥2l\documentclass[12pt]{minimal}
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\begin{document}$$r \ge 2 l$$\end{document}.
