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.
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Received July 8, 1998
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ID="*" Supported by NSF grant CCR98210-58 and ARO grant DAAH04-96-1-0013.
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Capalbo, M. Small Universal Graphs for Bounded-Degree Planar Graphs. Combinatorica 22, 345–359 (2002). https://doi.org/10.1007/s004930200017
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DOI: https://doi.org/10.1007/s004930200017