CSC274b
Spring 1998
Ileana Streinu

• Textbook, Chapter 1.1, pages 1-11: The Art Gallery Theorem, cont'd.
  • Points, lines, polygons. Convex and non-convex polygons. Simple closed curves and polygons. Jordan Curve Theorem. Mod n counting.
  • Visibility. Klee's Art Gallery problem. Max over min formulation. Experimentation. Chvatal's comb example: necessity of n/3 guards.
  • Triangulation of a polygon.
  • Graphs. Planar graphs.
  • Graph coloring. 3-coloring of triangulation graphs.
  • The pigeonhole principle.
  • Fisk's proof of Chvatal's Theorem: n/3 guards are sufficient.
• First problem set posted on web.