On Hamilton cycle decompositions of complete multipartite graphs which are both cyclic and symmetric
Date of Award
2021
Degree Name
Mathematics
College
College of Science
Type of Degree
M.A.
Document Type
Thesis
First Advisor
Dr. Michael Schroeder, Committee Chairperson
Second Advisor
Dr. Elizabeth Niese
Third Advisor
Dr. JiYoon Jung
Abstract
Let G be a graph with v vertices. A Hamilton cycle of a graph is a collection of edges which create a cycle using every vertex. A Hamilton cycle decomposition is cyclic if the set of cycle is invariant under a full length permutation of the vertex set. We say a decomposition is symmetric if all the cycles are invariant under an appropriate power of the full length permutation. Such decompositions are known to exist for complete graphs and families of other graphs. In this work, we show the existence of cyclic n-symmetric Hamilton cycle decompositions of a family of graphs, the complete multipartite graph Km×n where the number of parts, m, is odd and the part size, n, is also odd. We classify the existence where m is prime and prove the existence in additional cases where m is a composite odd integer.
Subject(s)
Graph theory.
Decomposition (Mathematics)
Recommended Citation
Akinola, Fatima A., "On Hamilton cycle decompositions of complete multipartite graphs which are both cyclic and symmetric" (2021). Theses, Dissertations and Capstones. 1356.
https://mds.marshall.edu/etd/1356
