# graph theory – What is the maximum number of marked squares on a 10×10 table s.t. every square has at most one marked neighbour?

There is a $$10 times 10$$ table of $$100$$ unit squares which squares can be marked or unmarked. We want to mark as many squares as possible s.t. every square (marked or unmarked) has at most one marked neighbour. Two squares are adjacent iff they have a common side or vertex.

What is the maximum number of marked squares under these conditions?