The reading list of MATH 262
Topics in Combinatorial Mathematics
Winter, 2015

1. We will use the book Spectral Graph Theory .
2. For the background information in graph theory, try Diestel's book.
3. For the background information in combinatorial probabilistic methods, try Spencer's book on Ten Lectures on the Probabilistic Method.
4. For generating functions, here is the book Generatingfunctionology by Wilf.
5. Here is the link to Analytic Combinatorics in Several Variables by Robin Pemantle and Mark Wilson.
6. For the background information in electric networks and random walks on grids, try Doyle's book on Random Walks and Electric Networks.
7. For the background information in random walks, try Aldous and Fill.

1. Finding sparse cuts via Cheeger inequalities for higher eigenvalues by Louis, Raghavendra, Tetali and Vempala.
2. Improved Cheeger's inequality: Analysis of spectral partitioning algorithms through higher order spectral gap by Kwok, Lau, Lee and Gharan.
3. Multi-way spectral partitioning and higher-order Cheeger inequalities by Lee, Gharan and Trevisan.
4. Multi-way expansion constants and partitions of a graph by Tanaka.
5. Partitioning into expanders by Gharan and Trevisan.
6. A spectral proof of the Regularity Lemma by Terry Tao. .
7. The 1999 paper Coverings, heat kernels and spanning trees.
8. A survey on expander graphs and their applications in 2006 by Hoory, Linial and Widgerson.
9. A website on applications of eigenvalues by Steve Butler.
10. Asymptopia by Joel Spencer.
11. Decomposing a graph into expanding subgraphs by Moshkovitz and Shapira
12. A survey on unique games conjecture by subhash Khot
13. A paper on small set expansion by Raghavendra, Steurer and Tetali.