Degree Conditions for Tight Hamilton Cycles

Abstrakt

We develop a framework to study minimum d-degree conditions in k-uniform hypergraphs, which guarantee the existence of a tight Hamilton cycle. Our main theoretical result deals with the typical absorption, path-cover and connecting arguments for all k and d at once, and thus sheds light on the underlying structural problems. Building on this, we show that one can study minimum d-degree conditions of k-uniform tight Hamilton cycles by focusing on the inner structure of the neighbourhoods. This reduces the matter to an Erdős–Gallai-type question for (k-d)-uniform hypergraphs.