Graduation Term
2023
Degree Name
Master of Science (MS)
Department
Department of Mathematics
Committee Chair
Amin Bahmanian
Abstract
Let $K_{n\times m}^h$ be the complete $h$-uniform $n$-partite hypergraph with parts of size $m$. A cycle of length $c$ in a hypergraph is an alternating sequences of distinct vertices, $v_i$, and distinct edges $e_i$ of the form $v_1, e_1, v_2, e_2, \dots , e_c, v_c$ such that $v_i, v_{i+1}\subseteq e_i$ and $v_{c+1}=v_1$. By applying the shadows of colored complexes, we nearly settle the problem of partitioning the edges of $K_{n\times m}^h$ into cycles of length $c$ where $c$ is a multiple of $m$. This is joint work with Amin Bahmanian and Max Ward.
Access Type
Thesis-Open Access
Recommended Citation
Madden, Genevieve, "Shadows of Colored Complexes and Cycle Decompositions of Equipartite Hypergraphs" (2023). Theses and Dissertations. 1685.
https://ir.library.illinoisstate.edu/etd/1685
DOI
https://doi.org/10.30707/ETD2023.20230711063201999230.999966