'n 3. (30 points) Let Kn be the complete graph on n vertices; that is, its...
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'n 3. (30 points) Let Kn be the complete graph on n vertices; that is, its edge-set consists of all possible unordered pairs of vertices. Suppose that some coloring of the edge-set of Kn is given. A triangle is called rainbow if it has at most one edge from each color. Show that there exists. a coloring of the edges of Kn using three colors with at least (3) rainbow triangles. 'n 3. (30 points) Let Kn be the complete graph on n vertices; that is, its edge-set consists of all possible unordered pairs of vertices. Suppose that some coloring of the edge-set of Kn is given. A triangle is called rainbow if it has at most one edge from each color. Show that there exists. a coloring of the edges of Kn using three colors with at least (3) rainbow triangles.
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