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Mar 26, 2011 at 15:04 comment added Ori Gurel-Gurevich I did mean that - it's a classic. The key word here is "simple" - no loops or multiple edges. Assume the graph is a triangulation (otherwise add edges). Then use Eular's formula + 2E=3F to get a bound on 2E/V which is the average degree.
Mar 26, 2011 at 12:44 comment added ght @ Ori: did you mean to say that "...any simple finite planar graph has average degree less than 6"? This is clearly not true!
Mar 26, 2011 at 5:54 history answered Ori Gurel-Gurevich CC BY-SA 2.5