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We study the equality of the extremal Betti numbers of the binomial edge ideal and those of its initial ideal in( ) for a closed graph . We prove that in some cases there is a unique extremal Betti number for in( ) and as a consequence there is a unique extremal Betti number for and these extremal Betti numbers are equal. K E Y W O R D SClosed graphs, binomial edge ideals, projective dimension, Betti numbers M S C ( 2 0 1 0 ) 05E40, 13C14, 13C15

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