On the average genus of a graph |
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Authors: | Jonathan L. Gross E. Ward Klein Robert G. Rieper |
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Affiliation: | 1. Department of Computer Science, Columbia University, 10027, New York, NY, USA
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Abstract: | 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 1 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 1. |
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