A Theorem on the Removal of Vertices from Blocks
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As my Senior Independent Project, I studied graph theory. After my preliminary studies, amid several abortive attempts to investigate problems which I found appealing, I was confronted with a conjecture by Jerome J. Karaganis, a graduate student at W.M.U., who hoped that it would help to prove Plummer's conjecture that the square of a block is hamiltonian. The former conjecture, Theorem 2 of this paper, would appear likely to have applications in other problems in which it is natural to use induction on the number of vertices. The Corollary could be used to show, for example, that it would be sufficient to prove Plummer's conjecture for blocks having at least one vertex of degree two, which may make the problem more accessible. It is believed that neither Theorem 2 nor the Corollary has appeared in the literature.With honors.