首页|Minimum degree thresholds for Hamilton (k/2)-cycles in k-uniform hypergraphs
Minimum degree thresholds for Hamilton (k/2)-cycles in k-uniform hypergraphs
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NSTL
Elsevier
For any even integer k > 6, integer d such that k/2 < d < k-1, and sufficiently large n is an element of (k/2)N, we find a tight minimum ddegree condition that guarantees the existence of a Hamilton (k/2)-cycle in every k-uniform hypergraph on n vertices. When n is an element of kN, the degree condition coincides with the one for the existence of perfect matchings provided by Rodl, Rucinski and Szemeredi (for d = k - 1) and Treglown and Zhao (for d > k/2), and thus our result strengthens theirs in this case. (c) 2021 Elsevier Inc. All rights reserved.
Hamilton cycleHypergraphAbsorbing methodRegularity lemmaDIRAC-TYPE THEOREMPERFECT MATCHINGSINTERSECTION-THEOREMSL-CYCLESSYSTEMS
NSTL
Elsevier
