Sandbox:DavidKohler/Alon try 1/to do list

Unless otherwise mentioned all references mentioned here are for the paper A proof of Alon's second eigenvalue conjecture and related problems published in the Memoirs of the American Mathematical Society.

• Definition of the distinction of self-loops into whole-loops and half-loops (see page 17).
• Definition of a W-labelling of an undirected graph (see page 17).
• Proof of theorem 3.5.
• Examples on page 21-22 why we need to update Shannon's algorithm in the first place.
• Add a visual example for the definition of irreducible eigenvalues.
• Proof of theorem 3.9.
• Proof of theorem 3.13.
• Program the proof of theorem 2.11 so that for fixed values of m and d it produces a d-regular graph G on n vertices which has λ₂(G) > 2√d - 1.
• create some standard for articles (like wikipedia's good articles) to keep track of the quality of the pages.
• finish last argument in theorem 4.2.