On the Problem of Partitioning Planar Graphs

TLDR: In this article, it was shown that every planar graph can be partitioned into two or more components of roughly equal size by deleting only $O( \sqrt{n} )$ vertices, and such a partitioning can be found in O( n )$ time.

Abstract: The results in this paper are closely related to the effective use of the divide-and-conquer strategy for solving problems on planar graphs. It is shown that every planar graph can be partitioned into two or more components of roughly equal size by deleting only $O ( \sqrt{n} )$ vertices, and such a partitioning can be found in $O ( n )$ time. Some of the theorems proved in the paper are improvements on the previously known theorems while others are of more general form. An upper bound for the minimum size of the partitioning set is found.