The Ramsey number.
Boza, Luis (2011)
The Electronic Journal of Combinatorics [electronic only]
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The Ramsey number.
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Let k and ℓ be positive integers with ℓ ≤ k − 2. It is proved that there exists a positive integer c depending on k and ℓ such that every graph of order (2k−1−ℓ/k)n+c contains n vertex disjoint induced subgraphs, where these subgraphs are isomorphic to each other and they are isomorphic to one of four graphs: (1) a clique of order k, (2) an independent set of order k, (3) the join of a clique of order ℓ and an independent set of order k − ℓ, or (4) the union of an independent set of...