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Consult discrete mathematics: prove that any simplicity with 6 vertices or its complement must contain a triangle.
Prove:

1) A graph with 6 vertices is G 1, and its complement is G2, so the complete graph G=? G 1∪G2 .

2) For the complete graph G, v 1 is connected with the other five vertices, let G 1 be represented by a red line and G2 by a blue line. For the five lines connected with other vertices of V 1, if they are expressed in two colors, then there must be a line with a color greater than or equal to 3, as shown in the figure, assuming that the number of red lines is greater than or equal to 3.

3) If any of the three sides (V2, V3), (V3, V4) and (V2, V4) in the graph is red, then there must be a triangle; If three sides are not red, they are blue. These three blue sides must form a triangle.

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