Abstract
A non-planar graph can only be planarized if it is structurally modified. This work presents a new heuristic algorithm that uses vertices deletion to modify a non-planar graph in order to obtain a planar subgraph. The proposed algorithm aims to delete a minimum number of vertices to achieve its goal. The vertex deletion number of a graph G = (V, E) is the smallest integer k � 0 such that there is an induced planar subgraph of G obtained by the removal of k vertices of G. Considering that the corresponding decision problem is NP-complete and an approximation algorithm for graph planarization by vertices deletion does not exist, this work proposes an evolutionary algorithm that uses a constructive heuristic algorithm to planarize a graph. This constructive heuristic has time complexity of O(n + m), where m = |V| and n = |E|, and is based on the PQ-trees data structure and on the vertex deletion operation. The algorithm performance is verified by means of case studies.
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