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Let k,n>0 be integers, and let D be a collection of n closed discs in the plane so that any point in R2 is contained
Let k,n>0 be integers, and let D be a collection of n closed discs in the plane so that any point in R2 is contained in at most k elements of D, and no disc of D is contained in another disc of D. The intersection graph I(D) of D is defined over the vertex set D, and its edges correspond to intersecting pairs D1,D2D. Show that for any weight function w:DR+{0} the intersection graph I(D) admits a weighted (9/10)-separator of size O(kn). Hint: What is the maximum degree of I(D)
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