For 1 ź d ź ź < k , we give a new lower bound for the minimum d-degree threshold that guarantees a Hamilton ź-cycle in k-uniform hypergraphs. When k ź 4 and d < ź = k - 1 , this bound is larger than the conjectured minimum d-degree threshold for perfect matchings and thus disproves a well-known conjecture of Rodl and Rucinski. Our (simple) construction generalizes a construction of Katona and Kierstead and the space barrier for Hamilton cycles.
['Jie Han', 'Yi Zhao']
Forbidding Hamilton cycles in uniform hypergraphs