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Discrete math
3. Consider the graph G on 6 vertices shown below: 2 Figure 1 Construct the complementary graph of G, say H. Find the crossing number of H. Solution: The graph H can be obtained by deleating the red edges in the complete graph in Figure 2
2 Figure 2 which form a subgraph isomorphic to G since it is a union of three disconnected edges. The graph left (H) is clearly a planar graph so its crossing number is 0.