Lower bounds for the average genus
Jianer Chen, Jonathan L. Gross, Robert G. Rieper · Journal of Graph Theory · 1995
Abstract Two lower bounds are obtained for the average genus of graphs. The average genus for a graph of maximum valence at most 3 is at least half its maximum genus, and the average genus for a 2‐connected simplicial graph other than a cycle is at least 1/16 of its cycle rank. © 1995 John Wiley & Sons, Inc.