K5 Graph Avoidance Coloring Game

226 Views Asked by At

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? 

1

There are 1 best solutions below

0
On

(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:

enter image description here