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Monochromatic Edges in Complete Multipartite Hypergraphs

Author

Listed:
  • Teeradej Kittipassorn

    (Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand)

  • Boonpipop Sirirojrattana

    (Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand)

Abstract

Consider the following problem. In a school with three classes containing n students each, given that their genders are unknown, find the minimum possible number of triples of same-gender students—not all of which are from the same class. Muaengwaeng asked this question and conjectured that the minimum scenario occurs when the classes are all boys, all girls and half-and-half. In this paper, we solve many generalizations of the problem including when the school has more than three classes, when triples are replaced by groups of larger sizes, when the classes are of different sizes, and when gender is replaced by other non-binary attributes.

Suggested Citation

  • Teeradej Kittipassorn & Boonpipop Sirirojrattana, 2022. "Monochromatic Edges in Complete Multipartite Hypergraphs," Mathematics, MDPI, vol. 10(13), pages 1-29, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2353-:d:856062
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    Keywords

    graph; hypergraph; coloring;
    All these keywords.

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