chapter 9cs4203/files/gt-lec12.pdf · 9.2 map-colorings 1 c 2010 b y jonathan l. gross. 2 chapter 9...

Chapter 9Graph Colorings A: Lec 129.1 Vertex-Colorings9.2 Map-Colorings

1 c 2010 by Jonathan L. Gross

2 Chapter 9 Graph Colorings A: Lec 12

9.1 VERTEX-COLORINGS

Minimization Problem for Vertex-Colorings

Fig 9.1.1

c 2010 by Jonathan L. Gross

Section 9.1 Vertex-Colorings 3

Fig 9.1.2



Fig 9.1.3

Modeling Applications as Vertex-Coloring



Sequential Vertex-Coloring Algorithm

Algo 9.1.1:



Fig 9.1.4

Fig 9.1.5



Basic Principles for Calculating ChromaticNumbers



Fig 9.1.6



Chromatic #s for Common Graph Families

Table 9.1.1



Chromatically Critical Subgraphs



Fig 9.1.7



Obstructions to -Chromaticity



Fig 9.1.8



Brooks’s Theorem


Section 9.2 Map-Colorings 21

9.2 MAP-COLORINGS



Fig 9.2.1

Fig 9.2.2



Dualizing Map-Colorings into V-Colorings

Fig 9.2.3



Geographic Maps

Figure 9.2.4



Fig 9.2.5



Fig 9.2.6



Fig 9.2.7



5-Color Thm for Planar Graphs and Maps

Fig 9.2.8



Fig 9.2.9



Fig 9.2.10



9.5 SUPPLEMENTARY EXERCISES


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