In case the author is reading, some places that could be clarified: > Scatter a bunch of points in a plane. Connect some of them with lines. That’s all a graph

In case the author is reading, some places that could be clarified: > Scatter a bunch of points in a plane. Connect some of them with lines. That’s all a graph is. This may mislead the uninitiated reader to think that the definition of a graph includes vertex locations in R^2. > Over the years, mathematicians worked to reduce the number of edges Hamiltonian graphs had to have. The article is about showing that certain graph properties guarantee the existence of a Hamiltonian cycle. But the logical structure of this sentence implies the converse: showing that the existence of a Hamiltonian cycle guarantees other properties. But all it guarantees is |E| >= |V|.