This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: 1 2. Graph coloring Find the chromatic numbers for the following graphs. G1: A B C D E G2: 1 5 3 4 2 Solution: The chromatic number for G1 is 3 and the chromatic number for G2 is 4. The following pictures show that the two graphs can be colored with this many colors. But we still need to argue that a smaller set of colors won’t work. G1 graph contains a cycle of 3 nodes (A, B, and C). So coloring with two colors is hopeless. G2 contains a set of four nodes (1,2,3,4) for which all pairs are connected. So it can’t be colored with less than four colors. G1: A:red B:blue C:green D:red E:blue G2: 1:red 5:blue 3:green 4:yellow 2:blue 2...
View Full Document
- Spring '08
- Graph Theory, Planar graph, g2, simple planar graph