LOWER BOUNDS FOR THE AVERAGE GENUS
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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 2connected simplicial graph other than a cycle is at least 1/16 of its cycle rank. 1995 John Wiley & Sons, Inc. Copyright 1995 Wiley Periodicals, Inc., A Wiley Company