By exploiting the properties of cactus graphs, proved the conjecture; however, the greedy embeddings constructed according to their proof are not necessarily planar embeddings, as they may include crossings between pairs of edges.
The greedy embeddings constructed according to their proof are exploiting the properties of cactus graphs. Cactus graphs are proved the conjecture; however. The greedy embeddings constructed according to their proof are not necessarily planar embeddings. They may include crossings between pairs of edges.