"Shadows of Colored Complexes and Cycle Decompositions of Equipartite H" by Genevieve Madden

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

DOI

https://doi.org/10.30707/ETD2023.20230711063201999230.999966

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