MATH 582

STRUCTURE OF GRAPHS, Spring 2012

Summary of Lectures

This page contains a summary of the lectures in this course for Spring 2012. It lists only the topics discussed in each lecture. The text provides extensive discussion and additional material, so no additional notes are given here.


1 1/18We: introduction (overview of topics)

Chapter 6: Elementary Structural Concepts
2 1/20Fr: Matrix Tree background, Matrix Arborescence Theorem, counting Eulerian circuits
3 1/23Mo: graceful labelings (hypercubes), T-decomposition (girth vs diameter), intro to packing
4 1/25We: graph packing (Sauer-Spencer Thms, Bollobas-Eldridge Conj, start of Hajnal-Szemeredi proof)
5 1/27Fr: completion of Hajnal-Szemeredi Theorem
6 1/30Mo: graphic and bigraphic lists (2-switch, Aigner-Triesch method)
7 2/01We: potentially k-edge-connected lists, Kundu's Theorem, vertex ptns under degree constraints
8 2/03Fr: graph reconstruction (counting arguments, disconnected graphs, tree preliminaries)
9 2/06Mo: reconstruction (trees, spanning subgraphs, almost all graphs), edge-reconstruction
10 2/08We: product dimension (examples and bounds)

Chapter 7: Connection and Cycles
11 2/10Fr: connectivity of cartesian products, Edmonds' Branching Theorem