Small Universal Graphs for Bounded-Degree Planar Graphs

For all positive integers N and k, let denote the family of planar graphs on N or fewer vertices, and with maximum degree k. For all positive integers N and k, we construct a -universal graph of size . This construction answers with an explicit construction the previously open question of the existence of such a graph. Received July 8, 1998 RID="*" ID="*" Supported by NSF grant CCR98210-58 and ARO grant DAAH04-96-1-0013.