Characterization of join graphs with crossing number zero (Q2743888)

The join \(G+H\) of two vertex-disjoint graphs \(G\) and \(H\) is obtained from the union of \(G\) and \(H\) by adding all edges between every vertex of \(G\) and every vertex of \(H\). The authors characterize all pairs \(G, H\) such that \(G+H\) is planar, outerplanar, and minimally nonouterplanar, respectively. The presentation of the paper is not very well. For example, the authors state some facts about an undefined term \(i(G)\) and use it in some places in their proofs, and the second sentence in the proof of Theorem 2.8 is not in the right ballpark.