**Combinatorial and Discrete Geometry: Sheet Y
Duals of Plane Graphs; Coloring**

Prepared by:

Joseph Malkevitch

Department of Mathematics and Computer Studies

York College (CUNY)

Jamaica, New York 11451

email: joeyc@cunyvm.cuny.edu

web page: http://www.york.cuny.edu/~malk

1. For each graph below:

a. Write down the face vector and degree sequence of the graph

b. Draw the (geometric) dual of the graph

c. Write down the face vector and degree sequence of the dual graph.

d. Find the vertex coloring number and face coloring number for each of the graphs and its dual.