Geodesic
Polynomial bounds for monochromatic tight cycle partition in \(r\)-edge-coloured \(K_n^{(k)}\)
Debmalya Bandyopadhyay1 ; Allan Lo1
1University of Birmingham
The electronic journal of combinatorics, Tome 32 (2025) no. 1
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

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 $r$.
DOI : 10.37236/13343
Classification : 05C70, 05C65, 05C35, 05C15
Mots-clés : \(k\)-uniform tight cycle, rainbow subgraphs

Debmalya Bandyopadhyay  1   ; Allan Lo  1

1 University of Birmingham 
@article{10_37236_13343,
     author = {Debmalya Bandyopadhyay and Allan Lo},
     title = {Polynomial bounds for monochromatic tight cycle partition in \(r\)-edge-coloured {\(K_n^{(k)}\)}},
     journal = {The electronic journal of combinatorics},
     year = {2025},
     volume = {32},
     number = {1},
     doi = {10.37236/13343},
     zbl = {1564.05300},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/13343/}
}
TY  - JOUR
AU  - Debmalya Bandyopadhyay
AU  - Allan Lo
TI  - Polynomial bounds for monochromatic tight cycle partition in \(r\)-edge-coloured \(K_n^{(k)}\)
JO  - The electronic journal of combinatorics
PY  - 2025
VL  - 32
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.37236/13343/
DO  - 10.37236/13343
ID  - 10_37236_13343
ER  - 
%0 Journal Article
%A Debmalya Bandyopadhyay
%A Allan Lo
%T Polynomial bounds for monochromatic tight cycle partition in \(r\)-edge-coloured \(K_n^{(k)}\)
%J The electronic journal of combinatorics
%D 2025
%V 32
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/13343/
%R 10.37236/13343
%F 10_37236_13343
Debmalya Bandyopadhyay; Allan Lo. Polynomial bounds for monochromatic tight cycle partition in \(r\)-edge-coloured \(K_n^{(k)}\). The electronic journal of combinatorics, Tome 32 (2025) no. 1. doi: 10.37236/13343

Cité par Sources :