Polynomial bounds for monochromatic tight cycle partition in $r$-edge-coloured $K_n^{(k)}$
| Autor: | Bandyopadhyay, Debmalya, Lo, Allan |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $K_n^{(k)}$ be the complete $k$-graph on $n$ vertices. A $k$-uniform tight cycle is a $k$-graph with its vertices cyclically ordered so that every $k$ consecutive vertices form an edge and any two consecutive edges share exactly $k-1$ vertices. A result of Bustamante, Corsten, Frankl, Pokrovskiy and Skokan shows that all $r$-edge coloured $K_{n}^{(k)}$ can be partitioned into $c_{r,k}$ vertex disjoint monochromatic tight cycles. However, the constant $c_{r,k}$ is of tower-type. In this work, we show that $c_{r, k}$ is a polynomial in $r$. Comment: 36 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|