Main Article Content
We show that every 4-uniform hypergraph with n vertices and minimum pair-degree at least (5/9+o(1))n^2/2 contains a tight Hamiltonian cycle. This degree condition is asymptotically optimal. In the proof we use a variant of the absorbing method and ideas from the proof of the optimal minimum vertex degree condition for tight Hamiltonian cycles in 3-uniform hypergraphs that was obtained in a previous work by Reiher, Rödl, Ruciński, Schacht, and Szemerédi.
How to Cite
Reiher, C., Rödl, V., Ruciński, A., Schacht, M., & Schülke, B. (2019). Minimum pair-degee for tight Hamiltonian cycles in 4-uniform hypergraphs. Acta Mathematica Universitatis Comenianae, 88(3), 1023-1027. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1296/757