Monochromatic paths in $2$-edge coloured graphs and hypergraphs

Maya Stein

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arXiv · 2204.12464

Monochromatic paths in $2$-edge coloured graphs and hypergraphs

Maya Stein

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Abstract

We answer a question of Gyárfás and Sárközy 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.

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Maya Stein. 2023-01-25. Monochromatic paths in $2$-edge coloured graphs and hypergraphs. https://arxiv.org/abs/2204.12464

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