The Oberwolfach Problem

My web browsing habits, especially my use of wikipedia, bears a striking similarity to the basic principles of Graph Theory: I begin with at a page—say, a list of mathematical concepts named after places—and eventually “command-click” my way down the blue hyperlink rabbit hole that ultimately and inevitably leads to an obscene number of tabs in my browser and hours of procrastination. Were I to plot a series click on a specific session, I would most likely use a directed graph. Each vertex would be a webpage and edges would point in the direction of which pages linked to which. This is one simple example of the many applications and analytical potential of graph theory.

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Investigation in Graph Theory and its Applications – Abstract

We live in an increasingly complex world with ever increasing interrelationships between seemingly separate aspects of life. Therefore, it seems that some of the greatest challenges we face are not necessarily in gathering or accessing information, but rather methodically organizing it in ways that will not only provide more efficient means by which to study said information, but also give rise to trends and patterns that we never thought to search for. Mathematics offers a wide array of tool that can be used as means to this end, be it statistics, probability, or other computational modeling. Another highly effective way of organizing and analyzing data is through the use of graphs (which can be simply defined as sets of objects that are connected by links: that is, vertices and edges). At its most basic level, graphs are immensely useful in organizing data from all disciplines. In Computer Science, graphs can be used to chart networks, flow of computation, etc. They are also immensely useful in Linguistics, where compositional semantics and syntax generally follow patterns that can be modeled through discrete mathematics. Other fields such as Chemistry, Physics, Economics, and Sociology also benefit from the use of graphs. So, in order to truly appreciate this branch of Mathematics, I will be studying Graph Theory and writing a report on what I have learned and how I can apply it not only in my Mathematics courses but also to the full scope of my liberal arts education.