3-Uniform 4-Path Decompositions of Complete 3-Uniform Hypergraphs

Author

Rachel McCannFollow

Date of Graduation

5-2022

Document Type

Thesis

Degree Name

Bachelor of Arts

Degree Level

Undergraduate

Department

Mathematical Sciences

Advisor/Mentor

Clay, Matt

Committee Member/Reader

Goodman-Strauss, Chaim

Committee Member/Second Reader

McComas, Kim

Committee Member/Third Reader

Kumar, T.K.S.

Abstract

The complete 3-uniform hypergraph of order v is denoted as K_v and consists of vertex set V with size v and edge set E, containing all 3-element subsets of V. We consider a 3-uniform hypergraph P₇, a path with vertex set {v₁, v₂, v₃, v₄, v₅, v₆, v₇} and edge set {{v₁, v₂, v₃}, {v₂, v₃, v₄}, {v₄, v₅, v₆}, {v₅, v₆, v₇}}. We provide the necessary and sufficient conditions for the existence of a decomposition of K_v into isomorphic copies of P₇.

Keywords

graph theory, hypergraph decomposition

Citation

McCann, R. (2022). 3-Uniform 4-Path Decompositions of Complete 3-Uniform Hypergraphs. Mathematical Sciences Undergraduate Honors Theses Retrieved from https://scholarworks.uark.edu/mascuht/4