Monochromatic paths in $2$-edge coloured graphs and hypergraphs
Combinatorics
2023-01-27 v3
Abstract
We answer a question of Gy\'arf\'as and S\'ark\"ozy from 2013 by showing that every 2-edge-coloured complete 3-uniform hypergraph can be partitioned into two monochromatic tight paths of different colours. We also give a lower bound for the number of tight paths needed to partition any 2-edge-coloured complete r-partite r-uniform hypergraph. Finally, we show that any 2-edge-coloured complete bipartite graph has a partition into a monochromatic cycle and a monochromatic path, of different colours, unless the colouring is a split colouring.
Cite
@article{arxiv.2204.12464,
title = {Monochromatic paths in $2$-edge coloured graphs and hypergraphs},
author = {Maya Stein},
journal= {arXiv preprint arXiv:2204.12464},
year = {2023}
}