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Variations of graphs in Ramsey theory are studied, in which not one, but multiple specified cliques are formed. Various walkthroughs of the construction and guaranteeing of such cliques, from the initial guaranteed conditions to the process of deduction of the other edge colourings are explained. We will not only be covering some simpler cases such as Ramsey’s theorem for small cliques such as triangles and \(K_{4}\) , but also about graphs with more vertices, and the possibility of guaranteeing more than 1 of the specific monochromatic cliques.

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On Ramsey Numbers and Monochromatic Cliques in a Complete Graph

  • 会议论文

  • 发表日期：

    2025年

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  • Akshat Vijoy,
  • Lawrence Juin Yi Loke,
  • Zheng Yu Choo,
  • Chan Lye Lee

摘要

Variations of graphs in Ramsey theory are studied, in which not one, but multiple specified cliques are formed. Various walkthroughs of the construction and guaranteeing of such cliques, from the initial guaranteed conditions to the process of deduction of the other edge colourings are explained. We will not only be covering some simpler cases such as Ramsey’s theorem for small cliques such as triangles and \(K_{4}\) , but also about graphs with more vertices, and the possibility of guaranteeing more than 1 of the specific monochromatic cliques.