An additive version of Ramsey’s theorem
نویسندگان
چکیده
منابع مشابه
An additive version of Ramsey’s theorem
We show that, for every r, k, there is an n = n(r, k) so that any r-coloring of the edges of the complete graph on [n] will yield a monochromatic complete subgraph on vertices { a+ ∑ i∈I di | I ⊆ [k] } for some choice of a, d1, . . . , dk. In particular, there is always a solution to x1 + . . .+ x` = y1 + . . .+ y` whose induced subgraph is monochromatic.
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ژورنال
عنوان ژورنال: Journal of Combinatorics
سال: 2011
ISSN: 2156-3527,2150-959X
DOI: 10.4310/joc.2011.v2.n4.a7