**Combinatorial and Discrete Geometry: Sheet I**

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 of the graphs below, solve the Chinese Postman Problem for the graph by finding an eulerization of the graph with as few duplicatications of existing edges as possible. Rememeber the other goal of eulerizing is to make every vertex even-valent. You can also check whether the solution you find is unique.

G:

H:

I: