Connection between the Pigeonhole Principle and Theorem 1
The Pigeonhole Principle and Theorem 1 are in fact special cases of a general mathematical theory: the Ramsey Theory.
If we put kn +1 balls in n boxes, then at least one box must contain k + 1 or more balls.
If we color kn +1 vertices by n colors, then there exists at least k + 1 vertices with the same color.
When all the edges of six vertices are colored by two colors, then there exists at least one triangle with the same color.
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