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Could anyone help me how to solve this?

We noted that every non-planar graph contains an edge so that if we erase this edge then the crossing number of the new graph is smaller.

• Is there a graph such that no matter which edge is deleted the crossing number of the new graph is smaller?

• Is there a graph such that no matter which edge is deleted the crossing number of the new graph reduces by two or more?

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    @Crostul the complete graph with $4$ vertices is planar... Draw a triangle, draw a vertex in the middle of the triangle. Include the remaining edges. – 2017-02-01
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    What about the complete graph with 5 vertices – 2017-02-01

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