Question 1 Proposition 1. A graph X is 2-colorable if and only if it is bipartite. Proof. If a graph X is 2-colorable, we can color it using colors a and b. Grouping vertices of color a in A and those of color b in B, we obtain two sets inside which no two vertices are adjacent. Conversly, if X is Bipartite, we can group the vertices in sets A and B. Simply color all vertices of A with color a ...