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
Daniel Gray
Abstract
We explore a relatively new concept in edge-colored graphs called conflict-free connectivity. A conflict-free path is a (edge-) colored path that has an edge with a color that appears only once. Conflict-free connectivity is the maximal number of internally disjoint conflict-free paths between all pairs of vertices in a graph. We also define the c-conflict-free-connection of a graph G. This is the maximum conflict-free connectivity of G over all c-colorings of the edges of G. In this paper we will briefly survey the works related to conflict-free connectivity. In addition, we will use the probabilistic method to achieve a bound on the c-conflict-free connection number of complete graphs.
OCLC Number
1102321993
Catalog Permalink
https://galileo-georgiasouthern.primo.exlibrisgroup.com/permalink/01GALI_GASOUTH/1fi10pa/alma9916234892602950
Recommended Citation
Wehmeier, Travis D., "Conflict Free Connectivity and the Conflict-Free-Connection Number of Graphs" (2019). Electronic Theses and Dissertations. 1897.
https://digitalcommons.georgiasouthern.edu/etd/1897
Research Data and Supplementary Material
No
