Given a (simple) graph G with n≥2 vertices v1,v2,…,vn and m≥1 edges, Joël and Robert play the following game with m coins:[*]Joël first assigns to each vertex vi a non-negative integer wi such that w1+⋯+wn=m.
[*]Robert then chooses a (possibly empty) subset of edges, and for each edge chosen he places a coin on exactly one of its two endpoints, and then removes that edge from the graph. When he is done, the amount of coins on each vertex vi should not be greater than wi.
[*]Joël then does the same for all the remaining edges.
[*]Joël wins if the number of coins on each vertex vi is equal to wi.Determine all graphs G for which Joël has a winning strategy. combinatoricsgraph theorywinning strategy