Flynn, Melissa (2017) The Largest Bond in 3Connected Graphs. Undergraduate thesis, under the direction of Haidong Wu from Mathematics, The University of Mississippi.

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Abstract
A graph G is connected if given any two vertices, there is a path between them. A bond B is a minimal edge set in G such that G − B has more components than G. We say that a connected graph is dual Hamiltonian if its largest bond has size E(G)−V (G)+2. In this thesis we verify the conjecture that any simple 3connected graph G has a largest bond with size at least Ω(nlog32) (Ding, Dziobiak, Wu, 2015 [3]) for a variety of graph classes including planar graphs, complete graphs, ladders, Mo ̈bius ladders and circular ladders, complete bipartite graphs, some unique (3,g) cages, the generalized Petersen graph, and some small hypercubes. We will also go further to prove that a variety of these graph classes not only satisfy the conjecture, but are also dual Hamiltonian.
Item Type:  Thesis (Undergraduate) 

Creators:  Flynn, Melissa 
Student's Degree Program(s):  B.S. in Mathematics 
Thesis Advisor:  Haidong Wu 
Thesis Advisor's Department:  Mathematics 
Institution:  The University of Mississippi 
Subjects:  Q Science > QA Mathematics 
Depositing User:  Melissa Flynn 
Date Deposited:  12 May 2017 15:18 
Last Modified:  12 May 2017 15:18 
URI:  http://thesis.honors.olemiss.edu/id/eprint/893 
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