Monochromatic Edges in Complete Multipartite Hypergraphs

Teeradej Kittipassorn and Boonpipop Sirirojrattana
Additional contact information
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

Mathematics, 2022, vol. 10, issue 13, 1-29

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.

Keywords: graph; hypergraph; coloring (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/13/2353/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/13/2353/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:13:p:2353-:d:856062

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().