Digital Commons Network^™

The Four Color Theorem: A Possible New Approach, Matthew Brady

All Student Theses and Dissertations

The goal of this thesis is to explore the topic of graph coloring and expand on existing ideas in the field of Graph Theory. These developments will then be used to provide a possible approach in proving the 4 – color theorem that was made famous by Guthrie in the 1800’s.

Since the theorem was presented, many proofs were presented and eventually disregarded for one reason or another. Today, the types of proofs that are considered correct all rely on a computer. The first of this kind was set forth by Appel and Haken in 1977. The driving idea behind …

Towards An Integrated Model Of The Mental Lexicon, Natawut Monaikul

All Student Theses and Dissertations

Several models have been proposed attempting to describe the mental lexicon-the abstract organization of words in the human mind. Numerous studies have shown that by representing the mental lexicon as a network, where nodes represent words and edges connect similar words using a metric based on some word feature, a small-world structure is formed. This property, pervasive in many real-world networks, implies processing efficiency and resiliency to node deletion within the system, explaining the need for such a robust network as the mental lexicon. However, each model considered a single word feature at a time, such as semantic or phonological …