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We prove that the red/blue edge-colouring of Kn that maximises the number of red-blue-red-blue cycles is obtained by taking an equipartition A, B of the vertex set, colouring every edge between A and B with one colour, and colouring all other edges with the other colour. Questions of this kind have links to Goodman’s bound on the minimum number of monochromatic triangles and to the inducibility problem of Pippenger and Golumbic.

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Maximising the Number of Properly 2-coloured 4-cycles

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  • 发表日期：

    2025年

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  • Abdul Basit,
  • Bertille Granet,
  • Daniel Horsley,
  • André Kündgen,
  • Katherine Staden

摘要

We prove that the red/blue edge-colouring of Kn that maximises the number of red-blue-red-blue cycles is obtained by taking an equipartition A, B of the vertex set, colouring every edge between A and B with one colour, and colouring all other edges with the other colour. Questions of this kind have links to Goodman’s bound on the minimum number of monochromatic triangles and to the inducibility problem of Pippenger and Golumbic.