Geodesic
Monochromatic paths in 2-edge-coloured graphs and hypergraphs
Maya Stein1
1Universidad de Chile
The electronic journal of combinatorics, Tome 30 (2023) no. 1
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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 k-partite k-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.
DOI : 10.37236/11465
Classification : 05C55, 05C38, 05C35, 05C65, 05D10, 05C70
Mots-clés : Ramsey theory, monochromatic paths, monochromatic cycles, edge colored hypergraphs, uniform complete hypergraphs

Maya Stein  1

1 Universidad de Chile 
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Maya Stein. Monochromatic paths in 2-edge-coloured graphs and hypergraphs. The electronic journal of combinatorics, Tome 30 (2023) no. 1. doi: 10.37236/11465

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