Work

Polynomial Bounds for Monochromatic Tight Cycle Partition in $r$-Edge-Coloured $K_n^{(k)}$

Year: 2025

Type: article

Abstract: 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 $r$.

Source: The Electronic Journal of Combinatorics

DOI: 10.37236/13343

Authors: Debmalya Bandyopadhyay, Allan Lo

Institution: University of Birmingham

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Engineering and Physical Sciences Research Council

Awards: Matchings and tilings in graphs, Ramsey theory: an extremal perspective