The Rado Path Decomposition Theorem
نویسندگان
چکیده
Fix c : [N] → r, an r-coloring of the pairs of natural numbers. An ordered list of distinct integers, a0, a1, a2 . . . ai−1, ai, ai+1 . . . is a monochromatic path for color k, if, for all i ≥ 1, c({ai−1, ai}) = k. The empty list is considered a path of any color k. Similarly the list of one element, a0, is also considered a path of any color k. For any monochromatic path of length two or more the color is uniquely determined. Paths can be finite or infinite. Since all paths considered in this article are monochromatic we will drop the word monochromatic.
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