A random version of the Burr-Erdős-Spencer theorem
Abstract
A well-known result of Burr, Erdős and Spencer [Transactions of the American Mathematical Society, 1975] determines the 2-colour Ramsey number for any sufficiently large collection of vertex-disjoint copies of a fixed graph H without isolated vertices. In this short note we prove a random version of this result, thereby generalising the random Ramsey theorem of Rödl and Ruciński [Journal of the American Mathematical Society, 1995].
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