Large planar graphs with given diameter and maximum degree
Discrete Applied Mathematics
Geometric Separator Theorems and Applications
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Maximum size of a planar graph with given degree and even diameter
European Journal of Combinatorics
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We analyse N-separators in planar weighted graphs for any integer N. The well-known result due to Lipton and Tarjan [5] is obtained in the case N=2. The existence of an N-separator is examined and the exact bounds for the best separation are demonstrated.