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Exploring Deep Graph Theory: Philosophical Implications in Graph Theory Statements

Deep Graph Theory delves into the philosophical implications of classical graph theory statements, questioning concepts like trees and forests. It challenges traditional definitions, such as considering a single tree as a forest. Future work includes converting caterpillar graphs to butterfly graphs and using graphs to predict success in football coaching.

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Exploring Deep Graph Theory: Philosophical Implications in Graph Theory Statements

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  1. A New Branch of Graph Theory Robbie Weber Joint work with John Thickstun

  2. Classical Graph Theory Spectral Graph Theory

  3. DEEP GRAPH THEORY

  4. What is Deep Graph Theory? • Takes graph theory statements out of context, and examines their philosophical implications.

  5. Example: Trees and Forests • Forest: an undirected, acyclic graph. • Tree: an undirected, acyclic, connected graph.

  6. Is It a Tree?

  7. Is It a Forest?

  8. Example: Trees and Forests • Forest: an undirected, acyclic graph. • Tree: an undirected, acyclic, connected graph.

  9. Every tree is a forest!

  10. Example: Trees and Forests • Forest: an undirected, acyclic graph. • Tree: an undirected, acyclic, connected graph. • We usually think of forests as a bunch of trees • That’s wrong! A single tree, on its own, is a forest.

  11. EVERY TREE IS A FOREST.

  12. Future work • Converting caterpillar graphs into butterfly graphs. • Using the Petersen graph to predict Coach Petersen’s success leading Washington football. • Think of more graph theory jokes non-theorists can understand.

  13. EVERY TREE IS A FOREST.

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