## Course Notes

Notes are in Microsoft Powerpoint format. They can be read on any of the Windows computers in the UCF labs, or, if you're on another computer and don't have Powerpoint, you can get a free viewer from Microsoft.

1. Introduction (Introduction to graphs and networks) - 17 pages (posted 8/27/2003; pages 1, 15 - 17 updated on 9/08/2003; page 15 slightly revised on 9/10/2003)

2. Connectivity of Graphs (Subgraphs, connected components, cut edges and cut vertices, connectivity, Hamilton circuits) - 20 pages (posted 9/08/2003; pages 8 - 10 added 9/10/2003; page 9 revised and pages 11 - 14 added 9/15/2003; typos on page 13 corrected, and pages 15 - 17 added 9/17/2003, page 14 revised on 9/20/2003; Fig 1(d) on page 16 corrected and pages 18 - 20 added 9/22/2003; the w(T) formula on page 18 corrected on 10/06/2003; some beginning lines and line 3 from the bottom of page 20 corrected on 10/07/2003)

3. Graph Representations and DFS (Adjacency matrix and adjacency list representations of graphs, depth-first search (DFS) of graphs, some applications) - 12 pages (posted 9/24/2003; page 3 revised after class on 9/24; pages 5 - 8 posted 9/29/2003; page 6 revised and two new pages added as page 8 and page 10, 10/01/2003; pages 11 and 12 added 10/13/2003; page 11 revised 10/15/2003)

4. Independent Sets, Covering, and Coloring (Independent sets, cliques, edge coloring, vertex coloring, chromatic number) - 17 pages (a link to Dr. Deo's textbook chapters added to page 1, 11/12/2003; pages 14 - 17 posted 11/03/2003; proof on page 12 revised 12/30/2003; page 13 posted and page 7 corrected 10/29/2003; pages 10 - 12 posted 10/27/2003; pages 7 - 9 posted 10/20/2003; pages 1 - 6 posted 10/15/2003)

5. Planar Graphs and Planarity Testing (Characterizations of planar graphs, geometric duals, planarity testing algorithms) - 7 pages (posted 11/05/2003; reposted with revisions on pages 5 and 6 on 11/07/2003; page 7 posted 11/12/2003)

6. Flow Networks (The max-flow, min-cut theorem, Ford-Fulkerson and Edmonds-Karp algorithms, min-cost flows and applications) 11 pages (a typo on page 10 corrected 11/20/2003; pages 9 - 11 posted 11/17/2003; page 8 and revised page 7 posted 11/12/2003; pages 1 - 7 posted 11/10/2003)

7. Matchings (Matchings in graphs, maximum bipartite matching, maximum-weight matching and assignment problems) 6 pages (posted 11/17/2003; page 3 revised and pages 4-6 added 11/19/2003; minor revisions to some pages 3-6 posted 12/09/2003)