Graph Avoidance Game
Two players take turns coloring the edges of the complete graph, $K_5$. The first player colors edges blue and the second player colors edges red. To win, the player must force their opponent to create a triangle with their colors.
I want to prove that the second player can always win.
Also, is it possible that some player can always force a red and blue C5?
(This is not an answer, but I need to post a graph.)
The question poser is not correct "that a draw isn't possible under $K_5$" as the following example illustrates: