"We cannot create new cycles by deleting a vertex" - How is this true within this context?:
"Assume G is planar and has girth at least 6. If v is a vertex of degree at most 2, then G-v still has girth at least 6."
For instance, as a counterargument, take a hexagon as a graph. If we remove a vertex, then I get a graph WITHOUT girth at least 6.