A minimum weighted degree above ((1+3t)/4)n suffices to force a perfect packing by K4s of total weight greater than 6t in every large edge-weighted complete graph.
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Packing tetrahedrons in edge-weighted graphs
A minimum weighted degree above ((1+3t)/4)n suffices to force a perfect packing by K4s of total weight greater than 6t in every large edge-weighted complete graph.