On Alternating 6-Cycles in Edge-Coloured Graphs
arXiv:2505.0980911.16 citationsh-index: 2
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Settles an open combinatorial problem for extremal graph theory researchers.
The authors prove that the number of alternating 6-cycles in a red/blue edge-coloured large clique is asymptotically maximized by a random colouring, solving the first open case of a problem by Basit et al.
In this short note, we use flag algebras to prove that the number of colour alternating 6-cycles in a red/blue colouring of a large clique is asymptotically maximized by a uniformly random colouring. This settles the first open case of a problem of Basit, Granet, Horsley, Kündgen and Staden.