• Wednesday, 8/28: Handed out handouts and basic info about the class. Described some basic problems from which graphs arrise. Started with definitions: graph, simple graph, bipartite graph, complement, neighbor, clique, independent set, chromatic number.
  
• Friday, 8/30: Defined some basic graphs (K_n, C_n, P_n), definitions of subgraphs, isomorphism, connected graphs, self-complementary graphs.
  
• Monday, 9/2: Labor Day - no class !
  
• Wednesday, 9/4: Decompositions, Petersen graph and its properties, adjacency matrix, incidence matrix.
  
• Friday, 9/6: Definitions of walks, trails and paths, components, König Theorem (characterization of bip. graphs), cut-edges, characterization of cut-edges.
  
• Monday, 9/9: walks, trails, Eulerian trails, Eulerian graphs (necessary and sufficient condition), degree-sum formula and applications.
  
• Wednesday, 9/11: hypercube Q_k and its properties, counting 6-cycles in Petersen graph, extremal problems.
  
• Friday, 9/13: existence of a bip. subgraph of a simple graph G with at least e(G)/2 edges, Mentel's Theorem, degree sequences, graphic sequences, Havel-Hakimi Theorem, definition of directed graphs.
• Monday, 9/16: 1.4 Directed graphs: basic definitions, connectivity (strong components, Eulerian digraph), de Bruijn cycles, tournaments and kings.
  
• Wednesday, 9/18: 2.1 Trees and Distance: basic definitions (tree, forest, spanning subgraph), characterization of trees (Lemma 2.1.3, Theorem 2.1.4), embedding of trees (Proposition 2.1.8)
  
• Friday, 9/20:
  
• Monday, 9/23: Pr\uuml;fer Code, counting spanning trees, Matrix Tree Theorem.
  
• Wednesday, 9/25: Kruskal's Algorithm and its proof, Prim's Algorithm, Dijkstra's ALgorithm.
  
• Friday, 9/27: Proof of Dijkstra's Algorithm, Breadth-First Search, Chapter 3. Matching and Factors: definitions (perfect, maximal, maximum) matching, alternating paths, augmenting paths, Berge's Theorem.
  
• Monday, 9/30: Proof of Berge's Theorem, matchings in bipartite graphs, Hall's Theorem and its proof.
• Wednesday, 10/2: König-Egerváry Theorem, edge and vertex covers, independent sets and their relations.
• Friday, 10/4: Gallai's Theorem and its proof, maximum bip. matching (Augmenting Path Algorithm), stable matchings.
• Monday, 10/7: Proposing algorithm for the stable matching and its proof, matchings in general graphs, Tutte's Theorem.
• Wednesday, 10/9: Proof of Tutte's Theorem, Berge-Tutte Formula, Peterson Theorem.
• Friday, 10/11: 2-factors in regular graphs, definitions of connectivity, connectivity of hypercube.
• Monday, 10/14: Harary graphs, edge-connectivity, relations between vertex-, edge-connectivity and min. degree,
• Wednesday, 10/16: bonds, blocks, 2-connected graphs and internally disjoint paths
• Friday, 10/18: Expansion lemma, equivalent conditions for 2-connectdness, ear decompositions.
• Monday, 10/14: closed ear decomposition and 2-edge-connected graphs, network and flows, f-augmenting paths and max. flows.

Last changed on October 21, 2002.