EXAMPLES THAT SATISFY BARNETTE'S CONJECTURE AND GENERAL ANALYSIS ON GRAPH THEORY AND HAMILTONICITY

In this paper, we take a closer look at Barnette's conjecture and at graph theory.This conjecture was named after professor David W. Barnette and states that every bipartite polyhedral graph with three edges per vertex has a Hamiltonian cycle.The complete definition of these terms in graph theory is included in our paper.We examine multiple types of graphs and polyhedral shapes and we proove or disproove them whether they satisfy the conjecture or not.Also, we worked on bipartite graphs, either complete or non-complete. We have constructed all the graphs on a Euclidean plane; we specifically studied planar cubic graphs.We explained every single aspect of the conjecture and we added some important examples.In addition, we represented almost all the graphs in two dimensional shapes, in order to study them more carefully.In conclusion, we did not manage to prove the conjecture , but our work might contribute a lot to future research on this specific topic.We included the references we used in our PDF file, at the end of our paper.We would like to think that this particular paper will help future researchers to find a valid and complete solution to this unsolved problem in mathematics.