DEGREE SEQUENCES OF GRAPHS AND DOMINANCE ORDER

Suppose that the graphical partition H(A) = (a(2)(1) greater than or e qual to ... greater than or equal to a(n)(1)) arises from A = (a(1) gr eater than or equal to ... greater than or equal to a(n)) by deleting the largest summand a(1) from A and reducing the a(1) largest of the r emaining summands by one. Let (a(i+1)(i) greater than or equal to ... greater than or equal to a(n)(i)) = H-i(A) denote the partition obtain ed by applying the operator H i times. We prove that the dominance ord er of partitions is preserved when we switch from A to (a(1) greater t han or equal to a(2)(1) greater than or equal to ... greater than or e qual to a(i+1)(i) greater than or equal to ...) =: E(A). This generali zes a recent result by Favaron, Maheo, and Sacle on the residue graph. (C) 1996 John Wiley & Sons, Inc.