1989 Reports

# On the Average Genus of a Graph

Not all rational numbers are possibilities for the average genus of an individual graph. The smallest such numbers are determined, and varied examples are constructed to demonstrate that a single value of average genus can be shared by arbitrarily many different graphs. It is proved that the number one is a limit point of the set of possible values for average genus and that the complete graph K4 is the only 3-connected graph whose average genus is less than one. Several problems for future study are suggested.

## Subjects

## Files

- cucs-482-89.pdf application/pdf 449 KB Download File

## More About This Work

- Academic Units
- Computer Science
- Publisher
- Department of Computer Science, Columbia University
- Series
- Columbia University Computer Science Technical Reports, CUCS-482-89
- Published Here
- January 11, 2012