A $k$-uniform tight cycle is a $k$-uniform hypergraph with a cyclic ordering of its vertices such that its edges are all the sets of size $k$ formed by $k$ consecutive vertices in the ordering.We prove that every red-blue edge-coloured $K_n^{(4)}$ contains a red and a blue tight cycle that are vertex-disjoint and together cover $n-o(n)$ vertices. Moreover, we prove that every red-blue edge-coloured $K_n^{(5)}$ contains four monochromatic tight cycles that are vertex-disjoint and together cover $n-o(n)$ vertices.
@article{10_37236_10604,
author = {Allan Lo and Vincent Pfenninger},
title = {Towards {Lehel's} conjecture for 4-uniform tight cycles},
journal = {The electronic journal of combinatorics},
year = {2023},
volume = {30},
number = {1},
doi = {10.37236/10604},
zbl = {1506.05154},
url = {http://geodesic.mathdoc.fr/articles/10.37236/10604/}
}
TY - JOUR
AU - Allan Lo
AU - Vincent Pfenninger
TI - Towards Lehel's conjecture for 4-uniform tight cycles
JO - The electronic journal of combinatorics
PY - 2023
VL - 30
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/10604/
DO - 10.37236/10604
ID - 10_37236_10604
ER -
%0 Journal Article
%A Allan Lo
%A Vincent Pfenninger
%T Towards Lehel's conjecture for 4-uniform tight cycles
%J The electronic journal of combinatorics
%D 2023
%V 30
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/10604/
%R 10.37236/10604
%F 10_37236_10604
Allan Lo; Vincent Pfenninger. Towards Lehel's conjecture for 4-uniform tight cycles. The electronic journal of combinatorics, Tome 30 (2023) no. 1. doi: 10.37236/10604
