Packing in a hypergraph: Difference between revisions

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==Packing under the stronger condition==
In 1997, [[Noga Alon]], [[Jeong Han Kim]], and [[Joel Spencer]] also supply a good bound for <math>\gamma</math> under the stronger <math>codegree</math> condition that every distinct pair <math>v, v'\in V</math> have at most one degeedge in common.
 
For a <math>k-</math>uniform, <math>D-</math>regular hypergraph on <math>n</math> vertices, if <math>k>3</math>, there exists a packing <math>P</math> covering all vertices but at most <math>O(nD^{-1/(k-1)})</math>. If <math>k=3</math> there exists a packing <math>P</math> covering all vertices but at most <math>O(nD^{-1/2}\ln^{3/2}D)</math>.