Question 3 Proposition
نویسنده
چکیده
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 and vertices of B with color b to obtain a proper 2-coloring. Remark 1. If X is a graph with chromatic number 2, then it is 2-colorable, and therefore it is bipartite.
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