Term of Award
Spring 2019
Degree Name
Master of Science in Mathematics (M.S.)
Document Type and Release Option
Thesis (open access)
Copyright Statement / License for Reuse
This work is licensed under a Creative Commons Attribution 4.0 License.
Department
Department of Mathematical Sciences
Committee Chair
Hua Wang
Committee Member 1
Colton Magnant
Committee Member 2
Goran Lesaja
Committee Member 3
Daniel Gray
Committee Member 3 Email
dagray@georgiasouthern.edu
Abstract
Given a graph $G$, we consider the problem of finding the minimum number $n$ such that any $k$ edge colored complete graph on $n$ vertices contains either a rainbow colored triangle or a monochromatic copy of the graph $G$, denoted $gr_k(K_{3}:G)$. More precisely we consider $G=B_{m,\ell}$ where $B_{m,\ell}$ is a broom graph with $m$ representing the number of vertices on the handle and $\ell$ representing the number of bristle vertices. We develop a technique to reduce the difficulty of finding $gr_{k}(K_{3}:B_{m,\ell})$, and use the technique to prove a few cases with a fixed handle length, but arbitrarily many bristles. Further, we find upper and lower bounds for any broom.
OCLC Number
1102321994
Catalog Permalink
https://galileo-georgiasouthern.primo.exlibrisgroup.com/permalink/01GALI_GASOUTH/1fi10pa/alma9916227589502950
Recommended Citation
Hamlin, Benjamin J., "Gallai-Ramsey Number for Classes of Brooms" (2019). Electronic Theses and Dissertations. 1896.
https://digitalcommons.georgiasouthern.edu/etd/1896
Research Data and Supplementary Material
No
