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math.CO2024
Clustered Colouring of Graph Products
Rutger Campbell, J. Pascal Gollin, Kevin Hendrey +5
A colouring of a graph has clustering if the maximum number of vertices in a monochromatic component equals . Motivated by recent results showing that many natural graph…
math.CO2024
When -intersecting hypergraphs admit bounded -strong colourings
Kevin Hendrey, Freddie Illingworth, Nina Kamčev +1
The -strong chromatic number of a hypergraph is the smallest number of colours needed to colour its vertices so that every edge sees at least colours or is rainbow. We show…
math.CO2024
A note on graphs of -colourings
Emma Hogan, Alex Scott, Youri Tamitegama +1
For a graph , the -colouring graph of has vertices corresponding to proper -colourings of and edges between colourings that differ at a single vertex. The graph su…