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Acta Mathematica Sinica, English Series

, Volume 34, Issue 12, pp 1795–1803 | Cite as

Some Ore-type Results for Matching and Perfect Matching in k-uniform Hypergraphs

  • Yi ZhangEmail author
  • Mei Lu
Article
  • 31 Downloads

Abstract

Let S1 and S2 be two (k − 1)-subsets in a k-uniform hypergraph H. We call S1 and S2 strongly or middle or weakly independent if H does not contain an edge eE(H) such that S1e ≠ ∅ and S2e ≠ ∅ or eS1S2 or eS1S2, respectively. In this paper, we obtain the following results concerning these three independence. (1) For any n ≥ 2k2k and k ≥ 3, there exists an n-vertex k-uniform hypergraph, which has degree sum of any two strongly independent (k − 1)-sets equal to 2n−4(k−1), contains no perfect matching; (2) Let d ≥ 1 be an integer and H be a k-uniform hypergraph of order nkd+(k−2)k. If the degree sum of any two middle independent (k−1)-subsets is larger than 2(d−1), then H contains a d-matching; (3) For all k ≥ 3 and sufficiently large n divisible by k, we completely determine the minimum degree sum of two weakly independent (k − 1)-subsets that ensures a perfect matching in a k-uniform hypergraph H of order n.

Keywords

Ore-type condition matching perfect matching hypergraph 

MR(2010) Subject Classification

05C65 05C70 

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Notes

Acknowledgements

We thank the referees for their time and comments.

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematical SciencesTsinghua UniversityBeijingP. R. China

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